Question

On a coordinate plane, 2 triangles are shown. Triangle L M N has points (negative 1, 3), (3, 1), and (negative 1, 1). Triangle L prime M prime N prime has points (negative 2, negative 1), (6, negative 5), and (negative 2, negative 5).
Which composition of similarity transformations maps TriangleLMN to TriangleL'M'N'?

a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation

Answer 1

Scale factor is 2 (distances double): LN = 2 (from y = 3 to y = 1) and L'N' = 4 (from y = -1 to y = -5), so k = 4/2 = 2 (>1).

Dilation by 2 about the origin sends
L(-1,3) -> (-2,6),
M(3,1) -> (6,2),
N(-1,1) -> (-2,2).

Then translate by (0, -7) (down 7): (-2,6)+(0,-7)=(-2,-1)=L', (6,2)+(0,-7)=(6,-5)=M', (-2,2)+(0,-7)=(-2,-5)=N'.

Thus: a dilation with scale factor greater than 1 and then a translation.