Question

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

Answer 1

Answer:

4567

983

4567*983

5865486

Answer 2

Let A = (7, 10), B = (-2, 5), C = (3,-4)

∴ AB = √{(7+2)²+(10-5)²} = √(9²+5²) = √81+25 =√106 units

BC = √{(-2-3)²+(5+4)²} = √{(-5)²+(9)²} = √25+81 =√106 units

CA = √{(3-7)²+(-4-10)²} = √{(-4)²+(-14)²} = √(16+196) = √212 units

Again,

AB² + BC² = (√106)²+(√106)² = 106+106 = 212 = CA²

∴ ΔABC is a right angle isosceles triangle with right angle at B.