Explanation:
the dilation by 3 with its center at (1, 0) means we need to imagine the direct lines between T and the center, U and the center, V and the center and W and the center, and make them 3 times as long.
that gives the new points.
(1, 0) to T is 2 units up, 3 units left.
3 times as long means 3×2 units up, 3×3 units left (all from the dilation center) :
(-3×3 + 1, 3×2 + 0) = (-8, 6) for new T.
it goes to the left (negative x side) and starts with 1 of (1, 0).
it goes up (positive y side) and starts with 0 of (1, 0).
(1, 0) to U is 1 unit down, 3 units left.
3 times as long means 3×1 unit down, 3×3 units left :
(-3×3 + 1, -3×1 + 0) = (-8, -3) for new U.
it goes to the left (negative x side) and starts with 1 of (1, 0).
it goes down (negative y side) and starts with 0 of (1, 0).
(1, 0) to V is 1 unit down, 2 units right.
3 times as long means 3×1 unit down, 3×2 units right :
(3×2 + 1, -3×1 + 0) = (7, -3) for new V.
it goes to the right (positive x side) and starts with 1 of (1, 0).
it goes down (negative y side) and starts with 0 of (1, 0).
(1, 0) to W is 2 units up, 2 units right.
3 times as long means 3×2 units up, 3×2 units right :
(3×2 + 1, 3×2 + 0) = (7, 6) for new W.
it goes to the right (positive x side) and starts with 1 of (1, 0).
it goes up (positive y side) and starts with 0 of (1, 0).
so, after dilation, the image of vertex T will be at (-8, 6).
the length of the image of side TU will be 3 times the length of TU.
the area of the image of TUVW will be 3×3 = 9 times the area of TUVW.
because for the area 2 lengths are multiplied. each length has the scaling factor of 3, so multiplying them gives the scaling factor 3×3 = 9 for the area.