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Chapter 1: Problem 17

Find the distance between the points. $$(-2,6),(3,-6)$$

Short Answer

Expert verified
The distance between the points (-2,6) and (3,-6) is 13 units.

Step by step solution

01

Identify Coordinates

Firstly, identify the coordinates of the two points. In this case, the coordinates of the first point are (-2,6) and the second point are (3,-6). So, x1 = -2, y1 = 6, x2 = 3 and y2 = -6.
02

Substitute into the formula

Substitute the coordinates into the distance formula. So, the distance = \(\sqrt{{(3 - (-2))^2 + ((-6) - 6)^2}}\).
03

Solve the Equation

Next, perform the arithmetic inside the parentheses, then square the results, and finally sum and take the square root: \(\sqrt{{(5)^2 + (-12)^2}} = \sqrt{{25 + 144}} = \sqrt{{169}}\).
04

Simplify the Square Root

Finally, simplify the square root. The square root of 169 is 13.

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