A transformation that maps triangle ABC onto triangle ADE is a dilation by a scale factor of 3 centered on point A.
This transformation that makes triangle ADE similar to triangle ABC based on the angle, angle (AA) similarity theorem.
In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size (dimensions) of a geometric object, but not its shape.
By critically observing the graph shown above, we can logically deduce that we have to move 4 units up and 1 unit to the right in order to go from point A to point B. Also, you must move 12 units up and 3 units to the right to go from point A to point D;
Scale factor = 3/1 = 12/4
Scale factor = 3.
Generally speaking, dilations preserve the shape and angle size of a geometric figure. Hence, angle ABC is congruent with angle ADE, and angle ACB is congruent with angle AED. Additionally, angle A is congruent to itself, so based on the angle, angle (AA) similarity theorem, triangle ABC is similar to triangle ADE;
∠ABC ≅ ∠ADE.
∠ACB ≅ ∠AED.
∠A ≅ ∠A.
ΔABC ~ ΔADE