Question

Given ∆ABC with vertices at (0, 5), (0, 0), and (-2, 0), and ∆DEF with vertices at (1, 0), (1, -5) and (x, y), find the value of x and y that makes ∆ABC ≅ ∆DEF.

Answer 1

First, we can see that AB and DE are parallel to the y-axis and have the same length of 5 units.

Next, we can see that BC and EF are parallel to the x-axis and have the same length of 2 units.

Finally, we can see that angle ABC is a right angle, since it is formed by the x-axis and the segment AB. Similarly, angle DEF is also a right angle, since it is formed by the x-axis and the segment DE.

Therefore, to make ∆ABC ≅ ∆DEF, we need to find the coordinates of the third vertex of ∆DEF that is congruent to (-2, 0) in ∆ABC. Since AB and DE are parallel to the y-axis, this vertex must also have an x-coordinate of -2. Since angle DEF is a right angle, this vertex must also lie on the line passing through (1, 0) and (1, -5), which is parallel to the y-axis. Therefore, the y-coordinate of this vertex is -2.

Hence, the coordinates of the third vertex of ∆DEF are (-2, -2).