Question

Point G is located at (3, -1) and point H is located at (-2, 3). Find the x value for the point that is the distance from point G to point H. (5 points)

1.5

-0.33

-0.5

6.33

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ G(\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad H(\stackrel{x_2}{-2}~,~\stackrel{y_2}{3})\qquad \qquad % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ x=\sqrt{[-2-3]^2+[3-(-1)]^2}\implies x=\sqrt{(-2-3)^2+(3+1)^2} \\\\\\ x=\sqrt{(-5)^2+4^2}\implies x=\sqrt{25+16}\implies x=\sqrt{41}\implies x\approx 6.4031$