Question

what is the distance between (-4, -1) and (6, 6)? provide an answer accurate to the nearest tenth.

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, \( x_1 = -4 \), \( y_1 = -1 \), \( x_2 = 6 \), \( y_2 = 6 \).

Step2: Substitute Values

Substitute into the formula: \( d = \sqrt{(6 - (-4))^2 + (6 - (-1))^2} = \sqrt{(10)^2 + (7)^2} \).

Step3: Calculate Squares

Compute \( 10^2 = 100 \) and \( 7^2 = 49 \), so \( d = \sqrt{100 + 49} = \sqrt{149} \).

Step4: Approximate Square Root

\( \sqrt{149} \approx 12.2 \) (since \( 12.2^2 = 148.84 \) and \( 12.3^2 = 151.29 \), so nearest tenth is 12.2).

Answer:

12.2