Q32 of 149 Page 14

Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.

Vertices of a quadrilateral are A (0, 0), B(5, 5) and C(-5, 5)

Using distance formula =

AB = = = units

BC = = = units

CA = = = units

Since AB = CA

Using Pythagoras theorem

BC² = AC² + AB²

100 = 50 + 50

100 = 100

Therefore vertices are of right isosceles triangle.

Find the point on x-axis which is equidistant from the points (-2, 5) and (2,-3).

Find the value of x such that where the coordinates of P, Q and R are (6,-1), (1, 3) and (x, 8) respectively.

If the point P(x, y) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.

Q (0, 1) is equidistant from P (5, -3) and R (x, 6), find the values of x. Also, find the distances QR and PR.