Question

given: y(-7, 7), z(-3, -9) find: yz

Explanation:

Step1: Recall the distance formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For points \(Y(-7, 7)\) and \(Z(-3, -9)\), let \(x_1=-7,y_1 = 7,x_2=-3,y_2=-9\).

Step2: Calculate the differences in coordinates

First, find \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-3-(-7)=-3 + 7 = 4\)
\(y_2 - y_1=-9 - 7=-16\)

Step3: Substitute into the distance formula

Substitute these values into the distance formula:
\(YZ=\sqrt{(4)^2+(-16)^2}=\sqrt{16 + 256}=\sqrt{272}\)

Step4: Simplify the square root

Simplify \(\sqrt{272}\):
Factor 272: \(272=16\times17\)
So \(\sqrt{272}=\sqrt{16\times17}=\sqrt{16}\times\sqrt{17}=4\sqrt{17}\)

Answer:

\(4\sqrt{17}\)