Question

what is the approximate distance between the points (-3, -4) and (-8, 1) on a coordinate grid?
a. 11.40 units
b. 12.08 units
c. 3.16 units
d. 7.07 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, $x_1=-3,y_1 = - 4,x_2=-8,y_2 = 1$.

Step2: Calculate differences

$x_2 - x_1=-8-(-3)=-8 + 3=-5$ and $y_2 - y_1=1-(-4)=1 + 4 = 5$.

Step3: Square differences and sum

$(x_2 - x_1)^2+ (y_2 - y_1)^2=(-5)^2+5^2=25 + 25=50$.

Step4: Calculate square - root

$d=\sqrt{50}\approx7.07$.

Answer:

D. 7.07 units