﻿  Find the distance between the points A and B in the following : (i) A(2, 3), B(4, 1)    (ii) A (a, b), B(-a, -b)    (iii) A(5, -8); B(-7, -3) (iv) A(4, 10), B(7, -6) (v) A (a + b, a - b), B(a - b, -a - b). from Mathematics Coordinate Geometry Class 10 CBSE

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Find the distance between the points A and B in the following :

(i) A(2, 3), B(4, 1)    (ii) A (a, b), B(-a, -b)    (iii) A(5, -8); B(-7, -3)

(iv) A(4, 10), B(7, -6) (v) A (a + b, a - b), B(a - b, -a - b).

Solution not provided. 541 Views

Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6, 2) arc the vertices of a square.

Given points are A(5, 6), B(1, 5), C(2, 1) and D(6,2). AC and BD are two diagonals of square. Fig. 7.24. Hence, diagonal

AC  = BD  = 162 Views

Show that (1, -1) is the centre of the circle circumscribing the triangle whose angular points are (4, 3), (-2, 3) and (6, -1).

Let the given points be P(4, 3), Q(-2, 3) and R(6, -1). Let 0(1, -1) be the centre of the circle. Fig. 7.25. Here, we have
OP = OQ = OR
⇒ O is equidistant from P, Q and R.
Hence ‘O’ is the centre of the circle circumscribing the triangle.

763 Views

The line joining the points (1, -2) and (-3, 4) is trisected. Find the co-ordinates of the points of trisection.

Case I. Fig. 7.28A.
Let the given points be A(3, -1) and B(-6, 5).
Let P and Q be the points of trisection of AB.
Then,    AP = PQ = QB = 1
Thus ‘P’ divides AB in the ratio 1 : 2.
Here, we have x1 = 1,    y1 = -2
x2 = -3,    y2 = 4
and    m1 = 1    m2 = 2
∴ The co-ordinates of ‘P’ are given by Case II. Fig. 7.29.
Now ‘Q’ divides AB in the ratio 2 : 1.
Here, we have x1 = 1,    y = -2
x2 = -3,    y2 = 4
and    m1 = 2    m2 = 1
∴ The co-ordinates of ‘Q’ are given by Hence, the co-ordinates of the points of trisection are 454 Views

Name the type of triangle formed, if any, by the following points and give reason for your answer: Let the given points be   Since, AB = BC
So, the given points form an isosceles triangle.

92 Views

The distance between the points (4, - 3) and (0, 0) is
• 4
• 5
• 7

C.

5
85 Views