Question

Find the distance between the two points in simplest radical form.
(-8,3) and (-2,-5)

Answer 1

Answer:   10 units

Work Shown:

Distance formula

$(x_1,y_1) = (-8,3) \text{ and } (x_2, y_2) = (-2,-5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-2))^2 + (3-(-5))^2}\\\\d = \sqrt{(-8+2)^2 + (3+5)^2}\\\\d = \sqrt{(-6)^2 + (8)^2}\\\\d = \sqrt{36 + 64}\\\\d = \sqrt{100}\\\\d = 10$

This distance value is exact.

Answer 2

Explaination :

Here we would be using distance formula to calculate the distance between those two points.

Points are,

• (-8,3)
• (-2,5)

★ Distance Formula :

• $\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar$

We have :

• x1 = -8
• x2 = -2
• y1 = 3
• y2 = -5

Substituting the values in the formula :

• Refer the attachment.