Question

directions: find the distance between each p

1. (-4, 6) and (3, -7)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \). Here, \( (x_1, y_1)=(-4, 6) \) and \( (x_2, y_2)=(3, -7) \).

Step2: Substitute values into formula

Calculate \( x_2 - x_1 = 3 - (-4)=7 \) and \( y_2 - y_1=-7 - 6=-13 \). Then \( d = \sqrt{7^2 + (-13)^2}=\sqrt{49 + 169}=\sqrt{218} \approx 14.76 \).

Answer:

The distance is \( \sqrt{218} \) (or approximately \( 14.76 \)).