## Verify that points P(-2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.

Given P(-2, 2), Q(2, 2) and R(2, 7).If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.By distance formula , distance between two points = √[(x2-x1)2+(y2-y1)2]PQ = √[(2-(-2))2+(2-2)2]PQ = √[(42+02]PQ = √16PQ […]

## Find the point on the X-axis which is equidistant from A(-3, 4) and B(1, -4).

Let C be the point on X axis equidistant from A(-3,4) and B(1,-4).Since C lies on X axis, the Y co-ordinate of C is 0.Let C = (x,0)Co-ordinates of A = (-3, 4)Co-ordinates of B = (1, -4)Since C is equidistant from A and B ,AC = BCBy distance formula, d(A,C) = √[(x2-x1)2+(y2-y1)2]d(A,C) = √[(x-(-3))2+(0-4)2]d(A,C) […]

## Determine whether the points are collinear.

(1) If the sum of any two distances out of d(A, B), d(B, C) and d(A, C) is equal to the third , then the three points A, B and C are collinear.we will find d(A, B), d(B, C) and d(A, C).Co-ordinates of A = (1,-3)Co-ordinates of B = (2,-5)Co-ordinates of C = (-4,7)By distance […]

## Find the distance between each of the following pairs of points.

(1) Let A(x1, y1) and B(x2 , y2) be the given pointsBy distance formula d(A,B) = √[(x2-x1)2+(y2-y1)2]Here x1 = 2, y1 = 3 , x2 = 4, y2 = 1d(A,B) = √[(4-2)2+(1-3)2]= √[22+(-2)2]= √8= 2√2Hence the distance between A and B is 2√2 units. (2) Let P(x1, y1) and Q(x2 , y2) be the given pointsBy distance formula d(P,Q) = √[(x2-x1)2+(y2-y1)2]Here […]