Question

1. give sequence of transformations that will abcd to figure a\b\c\d\

the square is moved to a(2,4), b(4,4), c(4,2) and d(2,2). name the transformation.
5.
a. translation b. reflection
c. rotation d. dilation

1. \\(\overline{ab}\\) with a(3,4) and b(-2,7) is reflected across the y-axis to form \\(\overline{ab}\\). determine the coordinates of b ?

a.(2,7) b.(2, -7)
c.(-2, -7) d.(-2,7)

1. \\(\delta abc\\) has the measures of \\(\angle a = 35^\circ\\), \\(\angle b = 103^\circ\\) and \\(\angle c = 42^\circ\\). \\(\delta abc\\) is reflected over a line that is 5 units away to create \\(\delta abc\\). what is the measure of \\(\angle b\\)?

a. 108° b. 98°
c. 205° d. 103°

Explanation:

Question 5

Step1: Recall transformation types

Translation: sliding a figure without rotation/reflection, coordinates change by same vector.
Reflection: flipping over a line, mirror image.
Rotation: turning around a point.
Dilation: resizing, changing side lengths.

Step2: Analyze the square's movement

Original square (let's assume original coordinates, e.g., if original A was (0,0), B(2,0), C(2,2), D(0,2)) moves to \( A'(2,4), B'(4,4), C'(4,2), D'(2,2) \). The x - coordinates increase by 2, y - coordinates increase by 4 (consistent shift, no flip/rotation/resizing). So it's a translation.

Step1: Recall reflection over y - axis rule

For a point \( (x,y) \), reflection over y - axis is \( (-x,y) \).

Step2: Apply rule to point B

Point \( B(-2,7) \). Using the rule, \( x=-2 \) becomes \( -(-2)=2 \), \( y = 7 \) remains. So \( B'(2,7) \).

Step1: Recall reflection property

Reflection is a rigid transformation, which preserves angle measures (and side lengths). So the image \( \triangle A'B'C' \) is congruent to \( \triangle ABC \).

Step2: Determine \( \angle B' \)

Since \( \angle B = 103^\circ \) and reflection preserves angles, \( \angle B'=\angle B = 103^\circ \).

Answer:

A. Translation

Question 6