Q45 of 149 Page 14

Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

Vertices of a quadrilateral are A (7, 10), B(-2, 5) and C(3, -4)

Using distance formula =

AB = = = units

BC = = = units

AC = = = units

Since AB = BC

Using Pythagoras theorem

AC² = AB² + BC²

212 = 106 + 106

212 = 212

Therefore vertices are of right isosceles triangle.

Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).

If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p.

If the point P (x, 3) is equidistant from the points A (7,-1) and B (6, 8), find the value of x and find the distance AP.

If A (3, y) is equidistant from points P (8, -3) and Q (7,6) , find the value of y and find the distance AQ.