Question

Maria claims that ΔABE ≅ ΔACD .

Select two of the transformations or series of transformations that support Maria's claim and maps ΔABE to ΔACD.

A dilation with a scale factor of 3 about point A.

A dilation with a scale factor of 2 about point B.

A dilation with a scale factor of 2 about point A followed by a translation of 4 units downward.

A dilation with a scale factor of 3 about point B followed by a translation of 4 units downward.

A dilation with a scale factor of 3 about point A followed by a translation of 8 units to the right.

A dilation with a scale factor of 2 about point B followed by a translation of 8 units to the right.

Answer 1

Two transformations or series of transformation that support Maria's claim and Maps ΔABE to ΔACD are;

A dilation with a scale factor of 3 about point A

A dilation with a scale factor of 3 about point B followed by a translation of 4 units downwards

Explanation:

Using an online source, we have;

ΔABE ~ ΔACD

The coordinate of triangle ΔABC are;

A(-6, 4), B(-6, 2), and E(-2, 2)

The coordinate of triangle ΔACD are;

A(-6, 4), C(-6, -2), and D(6, -2)

∠A ≅ ∠A by reflexive property

Segment BE ║Segment CD and segment DE and segment AE are collinear on transversal AD

∴ ∠E ≅ ∠D Corresponding angles

∴ ΔABE ~ ΔACD by Angle-Angle rule of congruency

Segment AB on ΔABE and segment AC on triangle ΔACD are corresponding sides on both triangles

The length of segment AB on ΔABE = 2 units

The length of segment AC on ΔACD = 6 units

The scale factor of dilation, SF = (The length of segment AC)/(The length of segment AB)

∴ SF = (6 units)/(2 units) = 3

Therefore, ΔABE maps to ΔACD by either of the following;

1) A dilation with a scale factor of 3 about point A

2) A dilation with a scale factor of 3 about point B followed by a translation of 4 units downwards.