Question

for the transformation shown to the right. angle 90 degrees, direction, counter - clockwise

1. (sbac) let r(3, 1) be a point on a polygon, and r be the corresponding point on a new image. the figure is translated by using (x, y)→(x - 1, y + 4) to arrive at r. what are the coordinates of r? the coordinates of r are (2,5)
2. (se) if the line (at the right) is reflected across the x - axis, which of the following is the graph of the new line?
3. lines m and n are parallel and cut by transversal p. determine if the statement true or false?

statement\ttrue\tfalse
∠1 and ∠4 are vertical angles
∠2 and ∠8 are corresponding angles
∠3 and ∠6 are alternate interior angles
∠5 and ∠7 make a linear pair

1. a triangle ∆abc with m∠a = 40, m∠b = 60, and m∠c = 80 is reflected across y - axis to obtain the ∆abc. what is the m∠c, in degrees?

Explanation:

Step1: Solve question 7

When a line is reflected across the x - axis, the y - coordinates of all points on the line change sign. If the original line has a positive slope and is above the x - axis in some parts, after reflection across the x - axis, it will have the same slope but be below the x - axis in the corresponding parts. Without seeing the original line's graph precisely, we know that the reflection across the x - axis will flip the line over the x - axis.

Step2: Solve question 8

• For the statement “∠1 and ∠4 are vertical angles”: Vertical angles are formed by two intersecting lines. ∠1 and ∠4 are formed by the intersection of lines m and p, so this statement is True.
• For the statement “∠2 and ∠8 are corresponding angles”: Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. ∠2 and ∠8 are not in the correct relative positions for corresponding angles, so this statement is False.
• For the statement “∠3 and ∠6 are alternate interior angles”: Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. ∠3 and ∠6 are between m and n and on opposite sides of p, so this statement is True.
• For the statement “∠5 and ∠7 make a linear pair”: A linear pair of angles are adjacent and supplementary. ∠5 and ∠7 are adjacent and their non - common sides form a straight line, so this statement is True.

Step3: Solve question 9

When a figure is reflected across an axis, the angle measures do not change. Since m∠C = 80° in △ABC, after reflecting △ABC across the y - axis to get △A'B'C', m∠C'=80°.

Answer:

1. (No specific answer given as original line graph not shown precisely, but concept explained for reflection across x - axis)

8.

• ∠1 and ∠4 are vertical angles: True
• ∠2 and ∠8 are corresponding angles: False
• ∠3 and ∠6 are alternate interior angles: True
• ∠5 and ∠7 make a linear pair: True

1. 80°