Advertisements
Advertisements
प्रश्न
Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)
उत्तर
Let P(x1, y1) = P(11, – 2), Q(x2, y2) = Q(4, – 3), R(x3, y3) = R(6, 3)
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((4 - 11)^2 + [-3 - (-2)]^2`
= `sqrt((-7)^2 + (-1)^2`
= `sqrt(49 + 1)`
= `sqrt(50)`
= `5sqrt(2)`
And
d(P, R) = `sqrt((x_3 - x_1)^2 + (y_3 - y_1)^2`
= `sqrt((6 - 11)^2 + [3 - (-2)]^2`
= `sqrt((-5)^2 + (5)^2`
= `sqrt(25 + 25)`
= `sqrt(50)`
= `5sqrt(2)`
Here, d(P, Q) = d(P, R)
∴ Point (11, – 2) is equidistant from (4, – 3) and (6, 3).
APPEARS IN
संबंधित प्रश्न
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Find the distance of a point P(x, y) from the origin.
If P (x , y ) is equidistant from the points A (7,1) and B (3,5) find the relation between x and y
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the distance of the following point from the origin :
(13 , 0)
Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .
A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
