Question

choose 1 answer: a $sqrt{85}$ b $sqrt{90}$ c 11 d 12

Explanation:

Step1: Determine the coordinates of the two points

The left - hand point has coordinates \((-5,8)\) and the right - hand point has coordinates \((4,6)\).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Let \((x_1,y_1)=(-5,8)\) and \((x_2,y_2)=(4,6)\). Then \(x_2 - x_1=4-(-5)=9\) and \(y_2 - y_1=6 - 8=-2\).

Step3: Calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\)

\((x_2 - x_1)^2+(y_2 - y_1)^2=9^2+(-2)^2=81 + 4=85\)

Step4: Find the distance \(d\)

Since \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), then \(d = \sqrt{85}\)

Answer:

A. \(\sqrt{85}\)