Question

find the distance between the pair of points (-2,5) and (7,-7). the exact distance is \boxed{} units. (type an exact answer, using radicals as needed.) the distance is approximately \boxed{} units. (round to the nearest hundredth as needed.)

Explanation:

Step1: Recall Distance Formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Here, \( x_1 = -2 \), \( y_1 = 5 \), \( x_2 = 7 \), \( y_2 = -7 \).

Step2: Substitute Values

Substitute into the formula: \( d = \sqrt{(7 - (-2))^2 + (-7 - 5)^2} = \sqrt{(9)^2 + (-12)^2} \).

Step3: Simplify Squares

Calculate squares: \( 9^2 = 81 \), \( (-12)^2 = 144 \). So, \( d = \sqrt{81 + 144} \).

Step4: Add Inside Square Root

Add: \( 81 + 144 = 225 \). Thus, \( d = \sqrt{225} = 15 \) (exact distance). The approximate distance is also 15 (since 15 is an integer).

Answer:

The exact distance is \( \boldsymbol{15} \) units. The distance is approximately \( \boldsymbol{15} \) units.