Question

which expression gives the distance between the points (4, 6) and (7, -3)?
a. $sqrt{(4 - 7)^2+(6 - 3)^2}$
b. $(4 - 7)^2+(6 + 3)^2$
c. $sqrt{(4 - 7)^2+(6 + 3)^2}$
d. $(4 - 7)^2+(6 - 3)^2$

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}$. Here, $x_1 = 4,y_1=6,x_2 = 7,y_2=-3$.

Step2: Substitute values

Substitute the values into the formula: $(x_1 - x_2)^2+(y_1 - y_2)^2=(4 - 7)^2+(6-(-3))^2=(4 - 7)^2+(6 + 3)^2$, and the distance is $\sqrt{(4 - 7)^2+(6 + 3)^2}$.

Answer:

C. $\sqrt{(4 - 7)^2+(6 + 3)^2}$