Question

what is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid?
a. 3.32 units
b. 7.81 units
c. 3.61 units
d. 2.23 units

Explanation:

Step1: Identify distance formula

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

Step2: Assign values

Let $(x_1,y_1)=(-5,1)$ and $(x_2,y_2)=(-2,3)$. Then $x_2 - x_1=-2-(-5)=3$ and $y_2 - y_1=3 - 1 = 2$.

Step3: Calculate squared - differences sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=3^2+2^2=9 + 4=13$.

Step4: Calculate distance

$d=\sqrt{13}\approx3.61$ (since $\sqrt{13}\approx3.60555\approx3.61$).

Answer:

C. 3.61 units