Question number 8. Tom drew a square on a coordinate plane. One of its diagonals lies on the x-axis. The coordinates of two vertices on the x-axis are negative 1 comma 0 and 5 comma 0. So here I have sketched a picture that probably looks similar to what Tom drew with coordinates marked here and the black line representing the x-axis. The question is which of the following are the coordinates of another vertex of this square? So here we have the vertex above the x-axis and the vertex below the x-axis and we have to find the coordinates of at least one of them. So what we notice is that we can draw in here a line connecting those two vertices here. That line will be perpendicular to the x-axis and these segments here will have equal length. So we can just average the coordinates to find the coordinate of the intersection here. And so what we have is there is going to be the x-coordinate and that is 5 plus negative 1 divided by 2. Their average gives us 2 and the y-coordinate is 0. So what we have is the point 2 comma 0. And then we see that the distance between 2 comma 0 and negative 1 0, that distance over here has to be 3 and it has to be the same distance as the distance over here from 2 comma 0 to 5. So that is 3. And then if we want a square, we know that the length of the other two line segments here, these two, have to be equal. They're equal to 3. And with that, we have a location of the coordinate below the x-axis. That point has coordinates 2 comma negative 3, which is not listed, but the one right above it, three units from the intersection point, has coordinates 2 comma 3 and that is listed as choice B. So that has to be our answer, 2 comma 3.

square

coordinate plane

diagonal

midpoint

vertex