The image of trapezoid PQRS after a reflection across Line W Y is trapezoid P'Q'R'S'.
2 trapezoids are shown. Line W Y is the line of reflection. Line segment R R prime has a midpoint at point Z. Line segment S S prime has a midpoint at point X.
What is m?
45º
90º
180º
270º
I think it's C
45
To determine the value of m, we need to understand the properties of a reflection.
When a figure is reflected across a line, the angle of reflection is equal to the angle of incidence (angle formed between the incident ray and the normal). In this case, the line of reflection is WY, and we need to find the angle of incidence for the segment RR'.
Since the line segment RR' has a midpoint at point Z, the line WY must be the perpendicular bisector of RR'. This means that the angle of incidence is formed by the line WY and the segment RR', and it is a right angle.
Therefore, the value of m is 90º.
To find the measure of the angle m, we need to understand the concept of angles formed by a reflection.
When a figure is reflected across a line, the angles formed by the original figure and its reflection are congruent (have the same measure).
In this case, we are given that trapezoid PQRS is reflected across line WY to form trapezoid P'Q'R'S'. We are looking for the measure of angle m.
Looking at the given information, we see that line segment RR' has a midpoint at point Z, and line segment SS' has a midpoint at point X. These midpoints are important because they help us understand the relationship between the angles in the original trapezoid (PQRS) and the reflected trapezoid (P'Q'R'S').
Since RR' is reflected across line WY to form R'R', we know that angle m (formed by RR' and WY) must be congruent to the reflected angle at R', denoted as m' (formed by R'R' and WY).
Similarly, since SS' is reflected across line WY to form S'S', the angle formed by SS' and WY, denoted as n, must be congruent to the reflected angle at S', denoted as n' (formed by S'S' and WY).
Therefore, the measure of the angle m is equal to the measure of angle m' and the measure of the angle n is equal to the measure of angle n'.
Since we are not given any specific angle measures, we cannot determine the exact measure of angle m. We can say that m is congruent to m' and n is congruent to n', but without additional information, we cannot find the measure of angle m.
So, the answer to the question "What is m?" is indeterminate without more information.