Question

if coordinates $(-2, -5)$ undergo a translation vector of $\langle 2, -3 \
angle$ in the coordinate plane, what would the resulting coordinates be? (1 point)
○ $(0, -8)$
○ $(0, -2)$
○ $(4, 2)$
○ $(4, -2)$

Explanation:

Step1: Recall translation rule

To translate a point \((x,y)\) by a vector \(\langle a,b
angle\), we use the rule \((x + a, y + b)\). Here, the original point is \((-2,-5)\) and the translation vector is \(\langle 2,-3
angle\), so \(x=-2\), \(y = -5\), \(a = 2\), \(b=-3\).

Step2: Calculate new x - coordinate

Calculate the new \(x\) - coordinate: \(x_{new}=x + a=-2+2 = 0\).

Step3: Calculate new y - coordinate

Calculate the new \(y\) - coordinate: \(y_{new}=y + b=-5+(-3)=-5 - 3=-8\).

Answer:

\((0,-8)\) (corresponding to the first option: \(\boldsymbol{(0, - 8)}\))