In the coordinate plane, rhombus LMNO has vertices L(–4,1), M(0,4), N(5,4), and O(1,1), and rhombus WXYZ has vertices W(–9,–1), X(–1,–7), Y(9,–7), and Z(1,–1).Select the sequence of transformations that can be applied to LMNO to show that it is similar to WXYZ.
Question
In the coordinate plane, rhombus LMNO has vertices L(–4,1), M(0,4), N(5,4), and O(1,1), and rhombus WXYZ has vertices W(–9,–1), X(–1,–7), Y(9,–7), and Z(1,–1).Select the sequence of transformations that can be applied to LMNO to show that it is similar to WXYZ.
Solution
To show that rhombus LMNO is similar to WXYZ, we can apply the following sequence of transformations:
-
Translation: Move rhombus LMNO down and to the left so that point L coincides with point W. This would involve translating all points of LMNO by (-5, -2).
-
Dilation: After the translation, we can see that WXYZ is twice as large as the translated LMNO. Therefore, we need to dilate LMNO by a factor of 2 with the center of dilation at the translated L (which is now at W).
-
Rotation: After the dilation, the shapes are congruent but not in the same orientation. We need to rotate the dilated LMNO 180 degrees about the center of dilation to match the orientation of WXYZ.
After these transformations, rhombus LMNO should coincide with WXYZ, showing that they are similar.
Similar Questions
In the coordinate plane, △JKL has vertices J(9,–3), K(3,5), and L(5,9), and △MNO has vertices M(–6,–3), N(6,6), and O(12,3).Select the sequence of transformations that can be applied to △JKL to show that it is similar to △MNO.
In the coordinate plane, △DEF has vertices D(3,–2), E(5,–3), and F(4,–4), and △GHI has vertices G(5,5), H(–5,0), and I(0,–3).Select the sequence of transformations that can be applied to △DEF to show that it is similar to △GHI.
REGULARITY Determine whether quadrilateral WXYZ is a rhombus, a rectangle, a square, a parallelogram, or none. Select all that apply. Explain. W(–3𝑊(–3 , 2)2) , X(2𝑋(2 , 5)5) , Y(4𝑌(4 , 2)2) , Z(–1𝑍(–1 , –2)–2)
In the coordinate plane, pentagon ABCDE has vertices A(7,3), B(9,–3), C(7,–5), D(1,–1), and E(3,5), and pentagon PQRST has vertices P(0,–2), Q(–1,1), R(0,2), S(3,0), and T(2,–3).Select the sequence of transformations that can be applied to ABCDE to show that it is similar to PQRST.a reflection across the x-axis, followed by a translation right 7 and down 1 and a dilation centered at the origin with scale factor 12a reflection across the x-axis, followed by a translation left 7 and up 1 and a dilation centered at the origin with scale factor 2a rotation of 180° centered at the origin, followed by a translation left 7 and up 1 and a dilation centered at the origin with scale factor 2a rotation of 180° centered at the origin, followed by a translation right 7 and down 1 and a dilation centered at the origin with scale factor 12Submit
Parallelogram W'X'Y'Z' is the image of parallelogram WXYZ after a dilation. WXYZ has coordinates W(–8,4), X(–4,8), Y(8,4), and Z(4,0). W'X'Y'Z' has coordinates W'(–6,3), X'(–3,6), Y'(6,3), and Z'(3,0).What are the scale factor and center of the dilation that maps WXYZ to W'X'Y'Z'?The scale factor is 34, and the center is the origin.The scale factor is 34, and the center is point W.The scale factor is 43, and the center is the origin.The scale factor is 43, and the center is point W.Submit
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.