Question

which is the image of ( p(-5, 11) ) along the vector ( langle 3, -8
angle )?

a) ( p(-8, 19) )

b) ( p(-8, 3) )

c) ( p(-2, -3) )

d) ( p(-2, 3) )

Explanation:

Step1: Recall translation formula

To find the image of a point \( P(x, y) \) along a vector \( \langle a, b
angle \), we use the translation formula \( P'(x + a, y + b) \).

Step2: Identify coordinates and vector components

Given \( P(-5, 11) \) and vector \( \langle 3, -8
angle \), so \( x = -5 \), \( y = 11 \), \( a = 3 \), \( b = -8 \).

Step3: Calculate new x-coordinate

New \( x \)-coordinate: \( -5 + 3 = -2 \)

Step4: Calculate new y-coordinate

New \( y \)-coordinate: \( 11 + (-8) = 3 \)
So the image \( P' \) is \( (-2, 3) \).

Answer:

D) \( P'(-2, 3) \)