Question

what is the distance between the following points? choose 1 answer: a $\sqrt{63}$

Explanation:

Step1: Identify the coordinates of the two points

The left - hand point has coordinates \((-2,7)\) and the right - hand point has coordinates \((6,9)\).

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

Here, \(x_1=-2,y_1 = 7,x_2=6,y_2 = 9\).
First, find \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2 - x_1=6-(-2)=6 + 2=8\)
\(y_2 - y_1=9 - 7=2\)
Then, find \((x_2 - x_1)^2+(y_2 - y_1)^2\):
\((x_2 - x_1)^2+(y_2 - y_1)^2=8^2+2^2=64 + 4=68\)

Step3: Calculate the distance

\(d=\sqrt{68}\)

Answer:

\(\sqrt{68}\)