Question

what is the shortest distance between the two points (1,5) and (-4,-7)? select the correct answer. √13 units 13 units √17 units 169 units

Explanation:

Step1: Identify distance - formula

The distance formula 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, $(x_1,y_1)=(1,5)$ and $(x_2,y_2)=(-4,-7)$.

Step2: Substitute values

$x_2 - x_1=-4 - 1=-5$, $y_2 - y_1=-7 - 5=-12$. Then $d=\sqrt{(-5)^2+(-12)^2}$.

Step3: Calculate squares and sum

$(-5)^2 = 25$, $(-12)^2 = 144$. So $d=\sqrt{25 + 144}=\sqrt{169}$.

Step4: Simplify square - root

$\sqrt{169}=13$.

Answer:

13 units