Your teacher will grade your responses for questions 9–10 to ensure that you receive proper credit for your answers.%0D%0AWhat part of the coordinate plane is equidistant from the points A(–3,2) and B(3,2)? Explain your answer.%0D%0A(2 points)
The part of the coordinate plane that is equidistant from the points A(-3, 2) and B(3, 2) is the line segment that lies on the y-axis between the points (-3, 0) and (3, 0).
To explain this, let's consider the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Given that the y-coordinate of both points A and B is 2, we can see that the only difference between the two points is the x-coordinate. Since the square of (x2-x1) will be zero, it means that the x-coordinate difference does not affect the distance between the two points.
Therefore, any point along the line segment on the y-axis between (-3, 0) and (3, 0) will have the same distance to both points A and B. This means that this line segment is equidistant from the two points.
Hence, the part of the coordinate plane that is equidistant from A(-3, 2) and B(3, 2) is the line segment on the y-axis between (-3, 0) and (3, 0).