Question

Two transformations are applied to the triangle to create triangle LMN so that MN and Mn Will both be parallel to the same access and Ln and l n Will both be parallel to the same axis which pair of trance formations will not result in these corresponding sides of the two triangles being parallel for the same axis?

Answer 1

Given the vertices of LMN:

L(-5, 1), M(-1, 5), N(-1, 1)

Given that two transformations are applied to triangle so that MN and M'N' will be parallel to the same axis. Also, LN and L'N' are parallel to the sma e axis.

Let's find the pair of transformations that will in result in this pair of corresponding sides not being parallel to the same axis.

Now, we are to find the pair of transoformations.

The set of transformations will be:

A rotation 90 degrees clockwise, followed by a translation 3 units down.

Apply the rotation rule for 90 degrees clockwise :

(x, y) ==> (y, -x)

Thus, we have:

L(-5, 1) ==> (1, 5)

M(-1, 5) ==> (5, 1)

N(-1, 1) ==> (1, 1)

After a translation 3 units down apply the rules of translation:

(x, y) ==> (x, y - 3)

Thus, we have:

(1, 5) ==> (1, 5 - 3) ==> (1, 2)

(5, 1) ==> (5, 1 - 3) ==> (5, -2)

(1, 1) ==> (1, 1 - 3) ==> (1, -2)

Therefore, the coordinates are:

L'(1, 2), M'(5, -2), N'(1, -2)

ANSWER:

A rotation 90° clockwise, followed by a translation 3 units down.