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)→(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 x - coordinate change

The rule for the x - coordinate is \(x
ightarrow x + 1\). This means for any point \((x,y)\) on the triangle, the new x - coordinate is obtained by adding 1 to the original x - coordinate. Adding 1 to the x - coordinate of a point shifts the point 1 unit to the right on the coordinate plane.

Step2: Analyze y - coordinate change

The rule for the y - coordinate is \(y
ightarrow y-3\). This means for any point \((x,y)\) on the triangle, the new y - coordinate is obtained by subtracting 3 from the original y - coordinate. Subtracting 3 from the y - coordinate of a point shifts the point 3 units down on the coordinate plane.

Answer:

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