Question

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Quadrilateral JKLM has vertices J(8, 4), K(4, 10), L(12, 12), and M(14, 10). Match each quadrilateral, described by its vertices, to the sequence of transformations that will show it is congruent to quadrilateral JKLM.

Answer 1

Answer:

Graphing the points, the answer would be the reflection since you would see that they are reflections to the x-axis because all x coordinates are the same, but y coordinates transformed into negative. So, this will give us, Quadrilateral J K L M with the following vertices:J(8, 4), K(4, 10), L(12, 12), and M(14, 10) is congruent to quadrilateral WXYZ with the following vertices: W(8, -4), X(4, -10), Y(12, -12), and Z(14, -10).Since you only look for the reflection and not all the transformations are needed.

Step-by-step explanation:

Answer 2

Answer:

1. W(5,1),X(1,7),Y(9,9) and Z(11,7).

2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).

3. E(5,6) ,F(1,12),G(9,14) and H(11,12).

4.O(10,1),P(6,7),Q(14,9) and R(16,7).

Step-by-step explanation:

We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)

We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM

1.a transformation 3 units down and 3 units left

By using transformation rule $(x,y)\rightarrow (x-3,y-3)$

The new  vertices  of quadrilateral is (5,1), (1,7),(9,9) and (11,7).

Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).

2.A sequence of reflection across x- axis and y-axis in order

Reflection across x- axis

The transformation  rule $(x,y)\rightarrow (x,-y)$

By using this rule

The vertices of quadrilateral are  (8,-4),(4,-10),(12,-12) and (14,-10).

After the reflection across y- axis

The transformations rule

$(x,y)\rightarrow (-x,y)$

By using this rule

We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).

Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).

3.a translation 3 unit left and 2 units up

The transformation rule $(x,y)\rightarrow (x-3,y+2)$

By using this rule

The new vertices are (5,6),(1,12),(9,14) and (11,12).

Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).

4.a translation 2 units right and 3 units down

The transformation rule

$(x,y)\rightarrow (x+2,y-3)$

By using this rule

The new vertices are (10,1),(6,7),(14,9) and (16,7)

Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).