ShmoopTube

00:03

Here’s your shmoop du jour…

00:06

Jake’s favorite way to mess with his roommate Blake is to continually move his stuff around.

00:10

Like… Blake’s unusual collection of signed… triangles.The triangle XYZ is shown below. 

00:16

If this triangle is translated +2 units on the x-axis and -2 units on the y-axis,

00:22

the resulting triangle X'Y'Z' would be which of the following figures shown on the same coordinate axis?

00:31

And here are the potential answers...

00:37

OK, so this question is asking us about translation.

00:40

A translation of 2 on the x-axis, the horizontal axis, moves the whole triangle to the right 2 units.

00:47

Similarly, a translation of negative 2 on

00:50

the y-axis, the vertical axis, means a shift of 2 units down for the entire triangle.

00:56

Since both translations move the entire triangle, this also means that any point on the triangle

01:01

XYZ undergoes the same translation.

01:04

We can focus on just one point of the triangle, like X, on the triangle XYZ.

01:09

It has coordinates (-4, 4).

01:12

Undergoing the translation of 2 to the right and 2 down, the new point, X', should have

01:16

coordinates (-4 + 2, 4 - 2) or (-2, 2).

01:22

The only triangle with X' having these coordinates is triangle D.

01:25

Our answer is D.

01:29

As in, "Don't touch my things!”

Full Transcript