RS Aggarwal solutions for Mathematics [English] Class 10 chapter 16 - Coordinate Geomentry [Latest edition]

Find the distance between the points

(i) A(9,3) and B(15,11)

Find the distance between the points

(ii) A(7,-4)and B(-5,1)

Find the distance between the points

A(-6,-4) and B(9,-12)

Find the distance between the points

A(1,-3) and B(4,-6)

Find the distance between the points

P(a + b,a - b)andQ(a -b,a + b)

Find the distance between the points

P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)

Find the distance of the following points from the origin:

(i) A(5,- 12)

Find the distance of  the following points from the origin:

(ii) B(-5,5)

Find the distance of  the following points from the origin:

(iii) C (-4,-6)

Find all possible values of x for which the distance between the points

A(x,-1) and B(5,3) is 5 units.

Find all possible values of y for which distance between the points is 10 units.

Find value of x for which the distance between the points P(x,4) and Q(9,10) is 10 units.

If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.

If the poin A(0,2)  is equidistant form the points B (3, p) and  C (p ,5) find the value of p. Also, find the length of AB.

Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Find the points on the y-axis which is equidistant form the points A(6,5)  and B(- 4,3) 

If the points p (x , y) is point equidistant from the points A (5,1)and B ( -1,5) , Prove that 3x=2y

If  p(x , y)  is point equidistant from the points A(6, -1)  and B(2,3) A , show that x – y = 3

Find the co-ordinates of the point equidistant from three given points A(5,3), B(5, -5) and C(1,- 5).

If the point A (4,3) and B ( x,5)  lies on a circle with the centre o (2,3) . Find the value of x.

If the point C ( - 2,3)  is equidistant form the points A (3, -1) and Bx (x ,8)  , find the value of x. Also, find the distance between BC

If the point P (2,2)  is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.

If the point ( x,y ) is equidistant form the points ( a+b,b-a ) and (a-b ,a+b ) , prove that bx = ay

Using the distance formula, show that the given points are collinear:  

 (1, -1), (5, 2) and (9, 5)

Using the distance formula, show that the given points are collinear:

(6, 9), (0, 1) and (-6, -7)

Using the distance formula, show that the given points are collinear:

(-1, -1), (2, 3) and (8, 11)

Using the distance formula, show that the given points are collinear:

(-2, 5), (0,1) and (2, -3)

prove  that the points A (7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.

Show that the points are the vertices of an isosceles right triangle.

If A(5,2), B(2, -2) and C(-2, t) are the vertices of a right triangle with ∠B=90° , then find the value of t .

Prove that the points A(2, 4), b(2, 6) and (2 +`sqrt(3)` ,5)  are the vertices of an equilateral triangle

Show that the points (-3, -3),(3,3) and C (-3 `sqrt(3) , 3 sqrt(3))` are the vertices of an equilateral triangle.

Show that the points A(-5,6), B(3,0) and C(9,8) are the vertices of an isosceles right-angled triangle. Calculate its area.

Show that the points O(0,0), A`( 3,sqrt(3)) and B (3,-sqrt(3))` are the vertices of an equilateral triangle. Find the area of this triangle.

Show that the following points are the vertices of a square:

(i) A (3,2), B(0,5), C(-3,2) and D(0,-1)

Show that the following points are the vertices of a square:

A (6,2), B(2,1), C(1,5) and D(5,6)

Show that the following points are the vertices of a square:

A (0,-2), B(3,1), C(0,4) and D(-3,1)

Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.

Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.

Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.

Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?

Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.

Prove that the points A(-4,-1), B(-2, 4), C(4, 0) and D(2, 3) are the vertices of a rectangle.

Show that the following points are the vertices of a rectangle.

A (2, -2), B(14,10), C(11,13) and D(-1,1)

Show that the following points are the vertices of a rectangle

A (0,-4), B(6,2), C(3,5) and D(-3,-1)

Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.

Find the co-ordinates of the point which divides the join of A(-5, 11) and B(4,-7) in the ratio 7 : 2

If A and B are (−2, −2) and (2, −4), respectively, find the coordinates of P such that `"AP" = 3/7 "AB"` and P lies on the line segment AB.

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.

Points P, Q, R and S divide the line segment joining the points A(1,2) and B(6,7) in five equal parts. Find the coordinates of the points P,Q and R

Points P, Q, and R in that order are dividing line segment joining A (1,6) and B(5, -2) in four equal parts. Find the coordinates of P, Q and R.

The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.

Find the coordinates of the midpoints of the line segment joining

A(3,0) and B(-5, 4)

Find the coordinates of the midpoints of the line segment joining 

P(-11,-8) and Q(8,-2)

If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.

The midpoint of the line segment joining A (2a, 4) and B (-2, 3b) is C (1, 2a+1). Find the values of a and b.

The line segment joining A( 2,9) and B(6,3)  is a diameter of a circle with center C. Find the coordinates of C

Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, -3) and B is (1, 4).

In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?

`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`

Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8) Also, find the value of m. 

Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.

In what ratio is the line segment joining A(2, -3) and B(5, 6) divide by the x-axis? Also, find the coordinates of the pint of division.

In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.

In what ratio does the line x - y - 2 = 0 divide the line segment joining the points A (3, 1) and B (8, 9)? 

Find the lengths of the medians of a  ΔABC whose vertices are A(0,-1) , B(2,1) and C (0.3).

Find the centroid of  ΔABC  whose vertices are A(-1, 0) B(5, -2) and C(8,2) 

If G(-2, 1) is the centroid of a  ΔABC  and two of its vertices are A(1, -6) and B(-5, 2) , find the third vertex of the triangle.

Find the third vertex of a  ΔABC if two of its vertices are B(-3,1)  and C (0,-2) and its centroid is at the origin

Show that the points A (3,1) , B (0,-2) , C(1,1)  and D (4,4) are the vertices of parallelogram ABCD.

If the points P (a,-11) , Q (5,b) ,R (2,15)  and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.

If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.

In what ratio does y-axis divide the line segment joining the points (-4, 7) and (3, -7)?

If the point `P (1/2,y)` lies on the line segment joining the points A(3, -5) and B(-7, 9) then find the ratio in which P divides AB. Also, find the value of y.

Find the ratio which the line segment joining the pints A(3, -3) and B(-2,7) is divided by x -axis Also, find the point of division.

The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.

Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.

ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P,Q,R and S be the midpoints of AB, BC, CD and DA respectively, Show that PQRS is a rhombus.

The midpoint P of the line segment joining points A(-10, 4) and B(-2, 0) lies on the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in which P divides CD. Also, find the value of y.

Find the area of  Δ ABC  whose vertices are: 

A (1,2) B (-2,3) and C (-3,-4)

Find the area of  ΔABC whose vertices are:
A(-5,7) , B (-4,-5) and C (4,5)

Find the area of  ΔABC whose vertices are:

A( 3,8) , B(-4,2) and C( 5, -1) 

Find the area of ΔABC  whose vertices are:

A(10,-6) , B (2,5) and C(-1,-3)

Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).

Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).

Find the area of quadrilateral ABCD whose vertices are A(-3, -1), B(-2,-4) C(4,-1) and D(3,4)

Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)

Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are A(2,1) B(4,3) and C(2,5)

A(7, -3), B(5,3) and C(3,-1) are the vertices of a ΔABC and AD is its median. Prove that the median AD divides ΔABC into two triangles of equal areas. 

Find the area of  ΔABC with A(1, -4) and midpoints of sides through A being (2, -1) and (0, -1).

A(6,1) , B(8,2) and C(9,4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ΔADE 

If the vertices of ΔABC  be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p

Find the value of k so that the area of the triangle with vertices A (k+1, 1), B(4, -3) and C(7, -k) is 6 square units

For what value of k(k>0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k+1, 10) equal to 53 square units?

Show that the following points are collinear:

(i) A(2,-2), B(-3, 8) and C(-1, 4)

Show that the following points are collinear:

A(-5,1), B(5, 5) and C(10, 7)

Show that the following points are collinear:

A(5,1), B(1, -1) and C(11, 4)

Show that the following points are collinear:

A(8,1), B(3, -4) and C(2, -5)

Find the value of x for which points A(x, 2), B(-3, -4) and C(7, -5) are collinear.

For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.

For what value of y, are the points P(1, 4), Q(3,y) and R(-3, 16) are collinear ?

Find the value of y for which the points A(-3, 9), B(2,y) and C(4,-5) are collinear.

For what values of k are the points A(8, 1) B(3, -2k) and C(k, -5) collinear.

Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7,5) are collinear.

Find a relation between x and y, if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

Prove that the points A (a,0), B( 0,b) and C (1,1) are collinear, if `( 1/a+1/b) =1`.

If the points P(-3, 9), Q(a, b) and R(4, -5) are collinear and a+b=1, find the value of a and b.

Find the area of ΔABC with vertices A(0, -1), B(2,1) and C(0, 3). Also, find the area of the triangle formed by joining the midpoints of its sides. Show that the ratio of the areas of two triangles is 4:1.

Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.

If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.

ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of one its diagonal.

If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.

Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, −3). Also, find the value of x.     

Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and D(2,6) are equal and bisect each other

Find the lengths of the medians of a ∆ABC whose vertices are A(7, –3), B(5,3) and C(3,–1)

If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value of k. 

Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)

`" Find the distance between the points"   A ((-8)/5,2) and B (2/5,2)`

Find the value of a, so that the point ( 3,a ) lies on the line represented by 2x - 3y =5 .

If the points  A(4,3)  and B( x,5) lie on the circle with center  O(2,3 ) find the value of x .

If P (x , y )  is equidistant from the points  A (7,1)  and B (3,5) find the relation between x and y

If the centroid of ΔABC having vertices  A (a,b) , B (b,c) and C (c,a) is the origin, then find the value of (a+b+c).

Find the centroid of ΔABC  whose vertices are A(2,2) , B (-4,-4) and C (5,-8).

In what ratio does the point C (4,5) divides the join of A (2,3)  and B (7,8) ?

 If the points  A (2,3),  B (4,k ) and C (6,-3) are collinear, find the value of k.