Question

find the distance between the points.

Explanation:

Step1: Determine coordinates of points

From the graph, \(P_1=(-5,5)\) and \(P_2=(4,1)\).

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

Here \(x_1=-5,y_1 = 5,x_2=4,y_2 = 1\).
Substitute into formula: \(d=\sqrt{(4-(-5))^2+(1 - 5)^2}\)

Step3: Simplify inside the square - root

\(4-(-5)=4 + 5=9\) and \(1-5=-4\)
\(d=\sqrt{9^2+(-4)^2}=\sqrt{81 + 16}\)

Step4: Calculate the sum and square - root

\(81+16 = 97\), so \(d=\sqrt{97}\approx9.85\)

Answer:

The distance between the points \(P_1\) and \(P_2\) is \(\sqrt{97}\approx9.85\)