Question

what are the coordinates of the point $(-1,4)$ after it is translated 3 units to the right and 2 units down?
a. $(2,6)$
b. $(-4,6)$
c. $(-4,2)$
d. $(2,2)$

Explanation:

Step1: Analyze horizontal translation

For a point \((x,y)\), translating right by \(a\) units changes \(x\) to \(x + a\). Here, \(x=-1\), \(a = 3\), so new \(x=-1+3 = 2\).

Step2: Analyze vertical translation

Translating down by \(b\) units changes \(y\) to \(y - b\). Here, \(y = 4\), \(b = 2\), so new \(y=4 - 2=2\).

Answer:

d. \((2,2)\)