Question

1. find the distance between a(-2,2) and b(-3,7). write your answer as a radical and as a decimal rounded to the nearest tenth.

Explanation:

Step1: Recall distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Step2: Identify coordinates

$x_1=-2,y_1 = 2,x_2=-3,y_2 = 7$

Step3: Substitute values

$d=\sqrt{(-3 + 2)^2+(7 - 2)^2}=\sqrt{(-1)^2+5^2}=\sqrt{1 + 25}=\sqrt{26}$

Step4: Calculate decimal

$\sqrt{26}\approx5.1$

Answer:

Radical: $\sqrt{26}$; Decimal: $5.1$