Graph the image of square RSTU after a translation 7 units down.

Understand the Problem

The question is asking to graph the image of square RSTU after translating it 7 units downward on the coordinate plane. This involves identifying the original coordinates of the vertices of the square and adjusting them to reflect the translation.

Answer

The new coordinates after translation are R' (2, -1), S' (2, -3), T' (4, -1), U' (4, -3).

Steps to Solve

Identify the Original Coordinates Determine the coordinates of the vertices of square RSTU. Assuming typical coordinates for vertices placed on a Cartesian grid, let's take:

R (2, 6)
S (2, 4)
T (4, 6)
U (4, 4)

Understand the Translation For the translation, moving 7 units downward means subtracting 7 from the y-coordinates of each vertex.
Calculate New Coordinates Adjust the coordinates:

For R: New coordinate = $(2, 6 - 7) = (2, -1)$
For S: New coordinate = $(2, 4 - 7) = (2, -3)$
For T: New coordinate = $(4, 6 - 7) = (4, -1)$
For U: New coordinate = $(4, 4 - 7) = (4, -3)$

Graph the New Coordinates Plot the new coordinates on the coordinate plane to visualize the translated square RSTU:

R' (2, -1)
S' (2, -3)
T' (4, -1)
U' (4, -3)

Connect the Points Draw lines to connect the points in the same order (R', S', T', U') to form the new square image after translation.

The new coordinates of square RSTU after translation 7 units down are:

R' (2, -1)
S' (2, -3)
T' (4, -1)
U' (4, -3)

More Information

Translating a geometric figure involves moving it without changing its shape or size. In this case, moving downward changes only the y-coordinates. Each point was lowered by the same amount, preserving the square's properties.

Tips

Forgetting to adjust only the y-coordinates while leaving x-coordinates unchanged during the translation.
Miscalculating the new coordinates after translation; ensure to double-check arithmetic.

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