Question

plot the image of point q under the translation ((x, y) \to (x + 1, y + 2)).

Explanation:

Step1: Find coordinates of Q

From the graph, point \( Q \) is at \( (-4, 4) \) (since it's 4 units left on x - axis and 4 units up on y - axis).

Step2: Apply translation rule

The translation rule is \( (x,y)\to(x + 1,y + 2) \). Substitute \( x=-4 \) and \( y = 4 \) into the rule.
For the x - coordinate: \( x+1=-4 + 1=-3 \)
For the y - coordinate: \( y + 2=4+2 = 6 \)
So the image of \( Q \) is at \( (-3,6) \). To plot this, move 3 units left of the origin on the x - axis and 6 units up on the y - axis.

Answer:

The image of point \( Q \) is at the coordinate \( (-3,6) \) (plotted by moving 1 unit right and 2 units up from the original point \( Q(-4,4) \)).