Answer:
See attached
Explanation:
You want to dilate the given triangle by a factor of 0.5 centered on the point (3, 1).
Dilation
Each point of the image is half as far from (3, 1) as the original point is. For example, the points on the preimage that are 8 units to the left of (3, 1) will be 4 units to the left in the dilated image.
The dimensions of the dilated triangle will be 0.5 times those of the original.
The dilated triangle is shown in red in the attachment.
__
Additional comment
It is often easiest to draw the dilated figure by counting grid squares on the graph. However, the coordinates can be computed using the transformation (for dilation factor k, center of dilation P) ...
(x, y) ⇒ (3, 1) +0.5((x, y) -(3, 1)) . . . . . . . . A ⇒ P +k(A -P) = kA +(1-k)P
(x, y) ⇒ (x+3, y+1)/2
For example,
(-5, -1) ⇒ (-5+3, -1+1)/2 = (-2, 0)/2 = (-1, 0)