Math Problem Statement

Solve the problems related to reflections involving a trapezoid and a parallelogram as given in the provided image.

Solution

Let's solve the problems visible in the image:

Problem 1 (Top Left):

Trapezoid QRST with vertices Q(4,1),R(6,1),S(8,6),T(2,6)Q(4, -1), R(6, -1), S(8, -6), T(2, -6) is reflected over the line x=1x = -1. What is the location of TT'?

To reflect a point across the vertical line x=1x = -1, the formula is: x=2(1)xx' = 2(-1) - x For point T(2,6)T(2, -6):

  • Apply the formula to the xx-coordinate: x=2(1)2=22=4x' = 2(-1) - 2 = -2 - 2 = -4
  • The yy-coordinate remains the same.

Thus, T(4,6)T'( -4, -6 ).

Problem 2 (Top Right):

Parallelogram STUV with vertices S(3,4),T(1,7),U(5,7),V(3,4)S(-3, 4), T(-1, 7), U(5, 7), V(3, 4) is reflected over the line y=xy = -x. What is the location of TT'?

When reflecting a point

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Reflection
Coordinate Geometry
Transformations

Formulas

Reflection across vertical line x = a: x' = 2a - x
Reflection across line y = -x: (x', y') = (-y, -x)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 8-10