Question

Find the distance between $(3,-5)$ and $(-4,7).$

• A. $\sqrt{144}$
• B. $\sqrt{193}$
• C. $\sqrt{169}$
• D. $\sqrt{133}$

Answer 1

The correct option is B $\sqrt{193}$

The distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

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

Therefore, the distance between the points $(3,-5)$ and $(-4,7)$ is:

$D=\sqrt{{(-4-3)}^2+{(7-(-5\left)\right)}^2}=\sqrt{{(-7)}^2+{12}^2}=\sqrt{49+144}=\sqrt{193}$