Question

question 3
1 pts
a translation moves a(-3,2) to a(0,0). find b, the image of b(5,4), under the same translation.
(7, 3)
(-8, -2)
(2, 6)
(8, 2)

Explanation:

Step1: Find translation vector

To find the translation vector, we subtract the coordinates of \( A \) from \( A' \). Let the translation vector be \( (h, k) \). For \( A(-3, 2) \) and \( A'(0, 0) \), we have \( h = 0 - (-3)=3 \) and \( k = 0 - 2=-2 \)? Wait, no, wait. Wait, translation is \( A + (h,k)=A' \), so \( (-3 + h, 2 + k)=(0,0) \). So solving for \( h \) and \( k \): \( -3 + h = 0\Rightarrow h = 3 \); \( 2 + k = 0\Rightarrow k=-2 \)? Wait, no, that would be if \( A' = A + (h,k) \). Wait, but let's check again. Wait, \( A(-3,2) \) to \( A'(0,0) \). So the change in \( x \)-coordinate is \( 0 - (-3)=3 \), change in \( y \)-coordinate is \( 0 - 2=-2 \). So the translation vector is \( (3, -2) \)? Wait, no, wait, maybe I got it reversed. Wait, translation is \( (x,y)\to(x + h, y + k) \). So \( -3 + h = 0\Rightarrow h = 3 \); \( 2 + k = 0\Rightarrow k=-2 \). So the translation is \( (x,y)\to(x + 3, y - 2) \).

Step2: Apply translation to B

Now, apply this translation to \( B(5,4) \). So \( x' = 5 + 3 = 8 \), \( y' = 4 - 2 = 2 \). So \( B' \) is \( (8,2) \).

Answer:

\( (8, 2) \) (corresponding to the option with \( (8,2) \))