Question

what is the formula to calculate the distance between two points on a coordinate plane?
a. $d=(x_2 - x_1)+(y_2 - y_1)$
b. $d=(x_2 + x_1)-(y_2 + y_1)$
c. $d = sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
d. $d=sqrt{(x_2 + x_1)^2+(y_2 + y_1)^2}$
what is the distance between points (1, 2) and (4, 6) on a coordinate plane?
a. $sqrt{29}$
b. $sqrt{25}$
c. $sqrt{32}$
d. $sqrt{20}$

Explanation:

Step1: Recall distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ on a coordinate plane is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. So the answer to the first question is C.

Step2: Identify coordinates

For the points $(1,2)$ and $(4,6)$, $x_1 = 1$, $y_1 = 2$, $x_2 = 4$, $y_2 = 6$.

Step3: Substitute values into formula

$d=\sqrt{(4 - 1)^2+(6 - 2)^2}=\sqrt{3^2+4^2}=\sqrt{9 + 16}=\sqrt{25}$.

Answer:

1. C. $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
2. B. $\sqrt{25}$