Question

given: q(-8, 2), r(-2, -10) find: qr

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1=-8,y_1 = 2,x_2=-2,y_2=-10\).

Step2: Substitute values into formula

Substitute the values into the formula:
\(QR=\sqrt{(-2 - (-8))^2+(-10 - 2)^2}\)
First, calculate the differences inside the square root:
\(-2-(-8)=-2 + 8 = 6\)
\(-10 - 2=-12\)

Step3: Square the differences

Square the results:
\(6^2 = 36\)
\((-12)^2=144\)

Step4: Sum the squares

Sum the squared values:
\(36+144 = 180\)

Step5: Simplify the square root

Simplify \(\sqrt{180}\):
\(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\)

Answer:

\(6\sqrt{5}\)