Question

point a is shown on the coordinate grid. the distance between point a and point b is 5 units. the x - coordinate of point b is -2. what is one possible y - coordinate of point b?

Explanation:

Step1: Identify coordinates of point A

From the graph, point A has coordinates $(-5,0)$. Let the coordinates of point B be $(-2,y)$.

Step2: Apply 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, $x_1=-5,y_1 = 0,x_2=-2,y_2=y$ and $d = 5$. Substitute these values: $5=\sqrt{(-2-(-5))^2+(y - 0)^2}$.

Step3: Simplify the equation

First, simplify $(-2-(-5))^2$: $-2-(-5)=-2 + 5=3$, so the equation becomes $5=\sqrt{3^2+y^2}=\sqrt{9 + y^2}$.

Step4: Solve for y

Square both sides of the equation: $25=9 + y^2$. Then subtract 9 from both sides: $y^2=25 - 9=16$. Take the square - root of both sides: $y=\pm4$. One possible value of y is 4.

Answer:

4