Question

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

Answer 1

Answer:

$|AC| = |BC| = \sqrt{29}$

Step-by-step 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.

$d = \sqrt{(x2 - x_1)^2 + (y_2 - y_1)^2}$

$|AC| = \sqrt{(-2 - 3)^2 + (-1 - 1)^2}$

$|AC| = \sqrt{(-5)^2 + (-2)^2}$

$|AC| = \sqrt{25 + 4}$

$|AC| = \sqrt{29}$

$|BC| = \sqrt{(-2 - 0)^2 + (-1 - 4)^2}$

$|BC| = \sqrt{(-2)^2 + (-5)^2}$

$|BC| = \sqrt{4 + 25}$

$|BC| = \sqrt{29}$

$|AC| = |BC| = \sqrt{29}$