Question

Show that the points A(−5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles triangle.

Answer 1

Let the given points be A(−5, 6), B(3, 0) and C(9, 8).

AB = `sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2`

= `sqrt((3 − (−5))^2 + (0 − 6)^2)`

= `sqrt((3 + 5)^2 + (−6)^2)`

= `sqrt((8)^2 + (−6)^2)`

= `sqrt(64 + 36)`

= `sqrt100`

= 10 units

BC = `sqrt((x_2 − x_1)^2 + ( y_2 − y_1)^2)`

= `sqrt ((9 − 3)^2 + (8 − 0)^2)`

= `sqrt((6)^2 + (8)^2)`

= `sqrt(36 + 64)`

= `sqrt100`

= 10 units

AC = `sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2`

= `sqrt((9 − (− 5))^2 + (8 − 6)^2)`

= `sqrt((9 + 5)^2 + (8 − 6)^2)`

= `sqrt((14)^2 + (2)^2)`

= `sqrt(196 + 4)`

= `sqrt200`

= `10 sqrt2  "units"`

Therefore, AB = BC

The points A(−5, 6), B(3, 0) and C(9, 8) are the vertices of an isosceles triangle.