Balbharati solutions for Geometry (Mathematics 2) [English] 10 Standard SSC Maharashtra State Board chapter 5 - Co-ordinate Geometry [Latest edition]

Find the distance between the following pairs of points:

(2, 3), (4, 1)

Find the distance between the following pairs of points:

(−5, 7), (−1, 3)

Find the distance between the following pair of points.

R(0, -3), S(0, `5/2`)

Find the distance between the following pair of points.

L(5, –8), M(–7, –3)

Find the distance between the following pair of point.

T(–3, 6), R(9, –10)

Find the distance between the following pairs of point.

W `((- 7)/2 , 4)`, X (11, 4)

Determine whether the points are collinear.

A(1, −3), B(2, −5), C(−4, 7)

Determine whether the points are collinear.

 L(–2, 3), M(1, –3), N(5, 4)

Determine whether the point is collinear.

R(0, 3), D(2, 1), S(3, –1)

Determine whether the point is collinear.

P(–2, 3), Q(1, 2), R(4, 1)

Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.

Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.

In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–3, 7), Q(1, –4), a : b = 2 : 1

In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.

 P(–2, –5), Q(4, 3), a : b = 3 : 4

In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.

P(2, 6), Q(–4, 1), a : b = 1 : 2

Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.

Find the centroid of the triangle whose vertice is given below.

(–7, 6), (2, –2), (8, 5)

Find the centroid of the triangle whose vertice is given below.

 (3, –5), (4, 3), (11, –4)

Find the centroid of the triangle whose vertice is given below.

(4, 7), (8, 4), (7, 11)

A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

Angle made by the line with the positive direction of X-axis is given. Find the slope of the line.

 45° 

Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.

 60°

Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.

 90°

Find the slope of the lines passing through the given point.

A(2, 3), B(4, 7)

Find the slope of the lines passing through the given point.

 P (–3, 1) , Q (5, –2) 

Find the slope of the lines passing through the given point.

C (5, –2) , D (7, 3)

Find the slope of the lines passing through the given point.

L (–2, –3) , M (–6, –8)

Find the slope of the lines passing through the given point.

 E(–4, –2) , F (6, 3)

Find the slope of the lines passing through the given point.

T (0, –3) , S (0, 4)

Determine whether the following point is collinear.
A(–1, –1), B(0, 1), C(1, 3)

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Determine whether the following point is collinear.

L(2, 5), M(3, 3), N(5, 1)

Determine whether the following point is collinear.

P(2, –5), Q(1, –3), R(–2, 3)

Determine whether the following point is collinear.

R(1, –4), S(–2, 2), T(–3, 4)

Determine whether the following point is collinear.

A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)

Fill in the blank using correct alternative.
Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be ........ .

Fill in the blank using correct alternative.

Out of the following, point ........ lies to the right of the origin on X– axis.

Fill in the blank using correct alternative.

Distance of point (–3, 4) from the origin is ______.

Fill in the blank using correct alternative.

A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is ______.

Determine whether the given point is collinear.

A (0, 2), B (1, -0.5), C (2, -3)

Determine whether the given point is collinear.

\[P\left( 1, 2 \right), Q\left( 2, \frac{8}{5} \right), R\left( 3, \frac{6}{5} \right)\]

Determine whether the given point is collinear.

 L(1,2), M(5,3) , N(8,6)

Find the distances between the following point.
A(a, 0), B(0, a)

Find the distances between the following point.

P(–6, –3), Q(–1, 9) 

Find the distances between the following point.

R(–3a, a), S(a, –2a)

In the following example, can the segment joining the given point form a triangle? If a triangle is formed, state the type of the triangle considering the side of the triangle.

L(6, 4), M(–5, –3), N(–6, 8)

In the following example, can the segment joining the given point form a triangle? If triangle is formed, state the type of the triangle considering side of the triangle.

 P(–2, –6) , Q(–4, –2), R(–5, 0)

In the following example, can the segment joining the given points form a triangle? If triangle is formed, state the type of the triangle considering sides of the triangle.

A(√2, √2), B(−√2, −√2), C(−√6, √6)

Find k if the line passing through points P(–12, –3) and Q(4, k) has slope \[\frac{1}{2}\].

Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2, 4) and D(1, 7).

Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.

Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.