What composition transformation rule has △LMN

Question

, L(1,1)
, M(7,2)
, and N(5,7)
map onto △L"M"N"
, L"(2,−1)
, M"(−4,0)
, and N"(−2,5)
?

Answer 1

The composition transformation rule that maps △LMN onto △L"M"N" is a translation.

To find the translation rule, we can calculate the difference in the x-values and the difference in the y-values between the corresponding points (L and L", M and M", N and N").

For L to L":
- The x-value of L" is 2, which is 1 unit greater than the x-value of L.
- The y-value of L" is -1, which is 2 units less than the y-value of L.

So, the translation rule for the x-values is +1 and for the y-values is -2.

For M to M":
- The x-value of M" is -4, which is 11 units less than the x-value of M.
- The y-value of M" is 0, which is the same as the y-value of M.

So, the translation rule for the x-values is -11 and for the y-values is 0.

For N to N":
- The x-value of N" is -2, which is 7 units less than the x-value of N.
- The y-value of N" is 5, which is the same as the y-value of N.

So, the translation rule for the x-values is -7 and for the y-values is 0.

Therefore, the composition transformation rule is:

△LMN → △L"M"N":
- x -> x + 1
- y -> y - 2