Question

∆ABC has coordinates for A(2, 6), B(2, 0) and C(7, 0). If ∆DEF has coordinates for D(2, -2) and E(2, -8), then what must be the coordinates for F to make the two triangles congruent?

Answer 1

To make ΔABC and ΔDEF congruent, point F must have the same relative position to point E as point C has to point B. This means moving 5 units to the right from E, leading to point F having coordinates (7, -8).

Step-by-step explanation:

To make two triangles congruent, they must have the same size and shape. For triangles ΔABC and ΔDEF to be congruent, we need to determine the coordinates of point F such that it mirrors the characteristics of point C from triangle ΔABC, considering that points D and E are given and mirror the locations of points A and B respectively.

First, we observe the coordinates of A and B: A(2, 6) and B(2, 0). We can see that they are vertically aligned since the x-coordinate is the same (2) and the difference in the y-coordinate is 6. Since D(2, -2) mirrors A, and E(2, -8) mirrors B, they too are vertically aligned with a difference of 6 in the y-coordinate.

Next, we look at the horizontal distance between B(2,0) and C(7,0), which is 5 units to the right (positive x-direction). To find point F, which mirrors C, we must also move 5 units to the right from point E. Therefore, since E has coordinates (2, -8), point F will have coordinates (2+5, -8) = (7, -8).