Question

A segment has endpoints at A(0,7) and B(9,0) as shown below. Which of the following represents the length of AB? (1) 16 (3) 63 A (2) V130 (4) V156 B

Answer 1

$(2)\text{ }\sqrt[]{130}$

Explanation

to solve this we can use the distance between 2 points formula:

$\begin{gathered} D_{12}=\sqrt[]{(x_2_{}-x_1)^2+(y_2-y_1)^2} \\ whereP1(x_1,y_1)\text{ is the initial point} \\ \text{and P}_2\text{ is the end point} \end{gathered}$

then,Let

Initial point= A=(0,7)

end point= B=(9,0)

now, replace in the formula

$\begin{gathered} D_{12}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D_{AB}=\sqrt[]{(9-0)^2+(0-7)^2} \\ D_{AB}=\sqrt[]{(9)^2+(-7)^2} \\ D_{AB}=\sqrt[]{81+49^{}} \\ D_{AB}=\sqrt[]{130} \\ \end{gathered}$

so, the answer is

$(2)\text{ }\sqrt[]{130}$

I hope this helps you