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Here’s your shmoop du jour… Jake’s favorite way to mess with his roommate
Blake is to constantly move his stuff around. Like… Blake’s unusual collection of signed…
triangles. The triangle XYZ is shown below.
If this triangle is translated +2 units on the x-axis and -2 units on the y-axis, the
resulting triangle X'Y'Z' would be which of the following figures shown on the same coordinate
axes? And here are the potential answers:
OK so this question is asking us about translation.
A translation of 2 on the x-axis, the horizontal axis, moves the whole triangle to the right
2 units. Similarly, a translation of negative 2 on
the y-axis, the vertical axis, means a shift of 2 units down for the entire triangle.
Since both translations move the entire triangle, this also means that any point on the triangle
XYZ undergoes the same translation. We can focus on just one point of the triangle,
like X, on the triangle XYZ. It has coordinates (-4, 4).
Undergoing the translation of 2 to the right and 2 down, the new point, X', should have
coordinates (-4 + 2, 4 - 2) or (-2, 2). The only triangle with X' having these coordinates
is triangle D. Our answer is D. As in… “Don’t touch
my things!”