Question

use the information to answer the question.
a triangle is graphed on the coordinate plane. one of the vertices is located at $(-4,4)$. the triangle will be translated using the rule $(x,y)\to(x + 1,y-3)$.
what affect will the translation have on the triangle?
a. the triangle will shift three units left and one unit up.
b. the triangle will shift three units right and one unit up.
c. the triangle will shift one unit left and three units down.
d. the triangle will shift one unit right and three units down.

Explanation:

Step1: Analyze the \(x\) - coordinate transformation

For a point \((x,y)\) in a coordinate - plane, when we have a transformation \((x,y)\to(x + 1,y-3)\), for the \(x\) - coordinate, if \(x\to x + 1\).
In the coordinate - plane, if \(x\) changes as \(x\to x + h\), when \(h>0\), the point moves \(h\) units to the right. Here \(h = 1\), so the point moves \(1\) unit to the right.

Step2: Analyze the \(y\) - coordinate transformation

For the \(y\) - coordinate, if \(y\to y-3\). In the coordinate - plane, if \(y\) changes as \(y\to y + k\), when \(k<0\), the point moves \(|k|\) units down. Here \(k=-3\), so the point moves \(3\) units down.

Since all the points of the triangle follow the rule \((x,y)\to(x + 1,y - 3)\), the entire triangle will shift one unit right and three units down.

Answer:

D. The triangle will shift one unit right and three units down.