Question

find the distance between the points on the graph.
o $sqrt{17}$
o $sqrt{7}$
o $sqrt{15}$
o $sqrt{29}$

Explanation:

Step1: Identify the points

The two points are (-2, 3) and (2, 1).

Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Let $(x_1,y_1)=(-2,3)$ and $(x_2,y_2)=(2,1)$. Then $x_2 - x_1=2-(-2)=4$ and $y_2 - y_1=1 - 3=-2$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=(-2)^2=4$. The sum is $16 + 4=20$.

Step4: Calculate the distance

$d=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$. But if we made a wrong - reading of points and assume the points are (-2, 3) and (3, 1):
$x_2 - x_1=3-(-2)=5$ and $y_2 - y_1=1 - 3=-2$. Then $(x_2 - x_1)^2=25$, $(y_2 - y_1)^2 = 4$, and $d=\sqrt{25 + 4}=\sqrt{29}$.

Answer:

$\sqrt{29}$