Question

find the distance between the two points rounding to the nearest tenth (if necessary). (8, 9) and (-1, -3)

Explanation:

Step1: Recall the 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, \( x_1 = 8 \), \( y_1 = 9 \), \( x_2=-1 \), \( y_2 = - 3 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=-1 - 8=-9 \) and \( y_2 - y_1=-3 - 9=-12 \). Then, substitute these into the formula: \( d=\sqrt{(-9)^2+(-12)^2} \).

Step3: Simplify the expression inside the square root

Calculate \( (-9)^2 = 81 \) and \( (-12)^2 = 144 \). Then, \( 81 + 144=225 \). So, \( d=\sqrt{225} \). Wait, no, wait, \( 81+144 = 225 \)? Wait, \( 81 + 144=225 \), but \( \sqrt{225}=15 \)? Wait, no, wait, \( (-9)^2=81 \), \( (-12)^2 = 144 \), \( 81+144 = 225 \), and \( \sqrt{225}=15 \). Wait, but let's check again. \( x_1 = 8 \), \( x_2=-1 \), so \( x_2 - x_1=-1 - 8=-9 \), squared is 81. \( y_1 = 9 \), \( y_2=-3 \), so \( y_2 - y_1=-3 - 9=-12 \), squared is 144. Sum is \( 81 + 144 = 225 \), square root of 225 is 15. So the distance is 15.0 (since we need to round to the nearest tenth, and 15 is a whole number, we can write it as 15.0).

Answer:

15.0