quadrilateral QRST with the coordinates Q (3, 1), R (4, 3), S (5, 3), and T (4, 0) is reflected over the line y = -1 what are the new coordinates of the image QRST. show your method

1 answer

To reflect the quadrilateral QRST across the line y=1, we need to apply the reflection formula for a point. The general rule for reflecting a point (x,y) across the line y=k is given by:

(x,y)=(x,2ky)

where (x,y) are the coordinates of the reflected point, and (x,y) are the original coordinates.

In our case, the line of reflection is y=1 (thus k=1). We will reflect each vertex of the quadrilateral.

  1. Reflect point Q (3, 1): y=2(1)1=21=3 Thus, the new coordinates of Q after reflection will be (3,3).

  2. Reflect point R (4, 3): y=2(1)3=23=5 So, the new coordinates of R after reflection will be (4,5).

  3. Reflect point S (5, 3): y=2(1)3=23=5 The new coordinates of S after reflection will be (5,5).

  4. Reflect point T (4, 0): y=2(1)0=20=2 Therefore, the new coordinates of T after reflection will be (4,2).

Now that we have reflected all the points, we can summarize the new coordinates of quadrilateral QRST after reflection over the line y=1:

  • Q' = (3,3)
  • R' = (4,5)
  • S' = (5,5)
  • T' = (4,2)

Thus, the new coordinates of the image QRST after reflection are:

  • Q(3,3)
  • R(4,5)
  • S(5,5)
  • T(4,2)