The coordinates of vertices of quadrilateral questions in picture

5.  (x, y) ⇒ (-x, y) — see attached for the diagram

6.  (x, y) ⇒ (x+3, y+5)

7.  dilation

Step-by-step explanation:

5. A point reflected across the y-axis will have the same y-value, but the opposite x-value. The transformation rule is ...

  (x, y) ⇒ (-x, y)

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6. A horizontal translation by "h" adds the value "h" to every x-coordinate. A vertical translation by "k" adds the value "k" to every y-coordinate. Then a translation by (h, k) will give rise to the rule ...

  (x, y) ⇒ (x+h, y+k)

Your translation right 3 and up 5 will give the rule

  (x, y) ⇒ (x+3, y+5)

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7. Any translation, rotation, or reflection is a "rigid" transformation that preserves all lengths and angles. Hence the transformed figure is congruent to the original.

When a figure is dilated, its dimensions change. It is no longer congruent to the original. (If the dilation is the same in x- and y-directions, then the figures are similar, but not congruent.)

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step-by-step explanation:

b. astronomers