Question

amy is trying to prove that a triangle with the vertices ( x(-6,2) ), ( y(-4,6) ), and ( z(-2,2) ) is an isosceles triangle. she found that side ( overline{xy} ) has a length of approximately 4.5 and that side ( overline{xz} ) has a length of 4. what is the length of side ( overline{yz} )? round your answer to one decimal place. (1 point) side ( overline{yz} ) has a length of

Explanation:

Step1: Identify coordinates of Y and Z

Y(-4,6), Z(-2,2)

Step2: Apply distance formula

$$\sqrt{(-2 - (-4))^2 + (2 - 6)^2} = \sqrt{(2)^2 + (-4)^2}$$

Step3: Calculate inside the square root

$$\sqrt{4 + 16} = \sqrt{20}$$

Step4: Compute and round

$$\sqrt{20} \approx 4.5$$

Answer:

4.5