Question

Explain why the two figures below are similar. Use complete sentences and provide evidence to support your explanation. (10 points)

Answer 1

The two figures are similar as the ratio of corresponding distances and slope of corresponding lines are EQUAL.

Explanation:

Noting the coordinates of points,

C(-1,6), D(3,4) , E(2,3) , F(3,0), G(1,-2) , A(0,1) , B(-2,2)

J(4.5,3.5), K(6.5,2.5), L(6,2), M(6.5,0.5) , N(5.5,-0.5) , H(5,1) , I(4,1.5)

using the distance formula =
`\sqrt{(x-x1)^(2) + (y-y1)^(2) }`

we find that,

CD=
`√(20)` and JK=
`√(5)`

thus, ratio of CD to JK is 2.

Similarly find ratio of DE to KL and so on, the ratio remains same.

Further one can even comment on the slopes of corresponding lines been equal.

Thus the figures turn out to be similiar to each other