Question

Points G (-5,-8) and H (3,7) are plotted on a coordinate grid.

What is the distance between points G and H?

Answer 1

17 units

Explanation:

`\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=√((x_2-x_1)^2+(y_2-y_1)^2)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}`

Given points:

• G (-5, -8)
• H (3, 7)

To find the distance between the given points G and H, substitute the given points into the distance formula:

`\begin{aligned}\implies d&=√((x_H-x_G)^2+(y_H-y_G)^2)\\&=√((3-(-5))^2+(7-(-8))^2)\\&=√((3+5)^2+(7+8)^2)\\&=√((8)^2+(15)^2)\\&=√(64+225)\\&=√(289)\\&=√(17^2)\\&=17\end{aligned}`

Therefore, the distance between points G and H is 17 units.

Answer 2

Answer: the distance between points G and H=17 units

Explanation:

Given: G(-5,-8) H(3,7)

Hence x₁=-5 x₂=3 y₁=-8 y₂=7

`\boxed{The\ distance\ L\ between\ points\ =√((x_2-x_1)^2+(y_2-y_1)^2) }`

`L=√((3-(-5))^2+(7-(-8))^2) \\\\L=√((3+5)^2+(7+8)^2) \\\\L=√(8^2+15^2) \\\\L=√(64+225) \\\\L=√(289) \\\\L=17\ units`