Question

Which transformation rule maps ​ triangle ABC ​ onto triangle DEF ?

Answer 1

Answer:  The correct option is (C) (x+7, y−3) .

Step-by-step explanation:  We are given to select the correct transformation rule that maps triangle ABC onto triangle DEF.

From the graph, we note that

the co-ordinates of the vertices of triangle ABC are A(-8, 6), B(-3, 6) and C(-7, 4).

And, the co-ordinates of the vertices of triangle DEF are D(-1, 3), E(4, 3) and F(0, 1).

The transformations from the vertices of triangle ABC to the vertices of triangle DEF are

A(-8, 6)   →   D(-1, 3) = D(-8+7, 6-3),

B(-3, 6)   →   E(4, 3) = E(-3+7, 6-3)

and

C(-7, 4)   →   F(0, 1) = F(-7+7, 4-3).

Therefore, the required transformation rule is given by

(x, y)  →  (x+7, y-3).

Thus, (C) is the correct option.

Answer 2

To find our solution, let us first take a point on one figure and match it with a point on the other figure. The easiest one is point C and point F. To get point C to point F, we first need to bring the x coordinate 7 units to the right, or, in other words, add 7. However, we are not yet at point F, as we need to decrease the y- value of point C by 3. Now, we are at point F. So, let's recap on what we did, we added the x by 7, and we subtracted the y value of point C by 3. 

We can turn this into words => (x + 7, y - 3).
Our answer is C) (x + 7, y - 3). Hope this helps and have a fantastic day!