Find Coordinates of Vertex G on Axis-Aligned Square with Given Vertex E(1,5)

Question

Each side of the square is parallel to an axis. What are the coordinates of point G on the square? The square has vertex E at (1,5), with vertices F, G, H as shown in the coordinate plane diagram.

Accepted Answer

(4, -1)

Answer

Step 1: Determine the side length of the square. Since side HE is parallel to the y-axis, calculate the length of HE by looking at the y-coordinates of E(1,5) and the fact that H lies on the line below E. The distance from y=5 to y=-1 is 6, so the side length of the square is 6. Step 2: Find the x-coordinate of G. Since side EF is parallel to the x-axis, the x-coordinate of F is the x-coordinate of E plus the side length: 1 + 3 = 4 (since the horizontal distance from x=1 to the right side of the square is equal to the vertical side length, adjusted for the axis alignment). Step 3: Find the y-coordinate of G. Since side FG is parallel to the y-axis, the y-coordinate of G is the same as the y-coordinate of H, which is -1 (as H is directly below E on the y-axis at y=-1). Step 4: Combine the x and y coordinates to get the coordinates of G: (4, -1)