Question

find the distance between points u and v in the coordinate plane.
a) ( 2sqrt{37} ) units
b) ( 2sqrt{17} ) units
c) ( 2sqrt{2} ) units
d) ( 4sqrt{13} ) units

Explanation:

Step1: Determine the coordinates of points

From the graph, we can see that the coordinates of point \(U\) are \((-7,-5)\) and the coordinates of point \(V\) are \((5,-3)\).

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1=-7,y_1 = -5,x_2=5,y_2=-3\) into the formula:

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Answer:

A. \(2\sqrt{37}\) units