Question

1. after translating a shape 2 units left and 3 units up, its new position is described by:

a. $(x + 2, y - 3)$
b. $(x - 2, y + 3)$
c. $(x - 3, y + 2)$
d. $(x + 3, y - 2)$

Explanation:

Step1: Recall translation rules

In coordinate geometry, translating a point \((x,y)\) \(h\) units left/right and \(k\) units up/down: left subtracts from \(x\), right adds to \(x\); up adds to \(y\), down subtracts from \(y\).

Step2: Apply left and up translation

Translating 2 units left: \(x\) - coordinate becomes \(x - 2\). Translating 3 units up: \(y\) - coordinate becomes \(y + 3\). So the new position is \((x - 2, y + 3)\).

Answer:

b. \((x - 2, y + 3)\)