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. \\(\triangle abc\\) has the measures of \\(\angle a = 35^\circ\\), \\(\angle b = 103^\circ\\) and \\(\angle c = 42^\circ\\). \\(\triangle abc\\) is reflected over a line that is 5 units away to create \\(\triangle 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. Reflection: flipping over a line. Rotation: turning around a point. Dilation: resizing.

Step2: Analyze coordinates

Original square (assume A(0,0), B(2,0), C(2,-2), D(0,-2)) 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). So it's translation.

Step1: Reflection over y - axis rule

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

Step2: Apply to point B(-2,7)

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

Step1: Reflection property

Reflection is a rigid transformation, so corresponding angles in the image and pre - image are equal.

Step2: Find \(\angle B'\)

In \(\triangle ABC\), \(\angle B = 103^{\circ}\). After reflection, \(\angle B'=\angle B = 103^{\circ}\).

Answer:

A. Translation

Question 6