Question

By calculating |AC| and |BC| , show that |AC| =|BC|​

Answer 1

`|AC| = |BC| = √(29)`

Explanation:

We are given the coordinates of points A, B, and C.

A(3, 1)

B(0, 4)

C(-2, -1)

Now we use the distance formula to find each length.

`d = √((x2 - x_1)^2 + (y_2 - y_1)^2)`

`|AC| = √((-2 - 3)^2 + (-1 - 1)^2)`

`|AC| = √((-5)^2 + (-2)^2)`

`|AC| = √(25 + 4)`

`|AC| = √(29)`

`|BC| = √((-2 - 0)^2 + (-1 - 4)^2)`

`|BC| = √((-2)^2 + (-5)^2)`

`|BC| = √(4 + 25)`

`|BC| = √(29)`

`|AC| = |BC| = √(29)`