Question

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Part 1
Reasoning  Find the lengths of the sides of rectangle ABCD shown on the coordinate plane. Suppose you double the length of each side. What would be the new coordinates of point C if the coordinates of point A stay the same​? Use pencil and paper to explain your reasoning.
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Part 1
Sides AB and CD are each
  
enter your response here units long.

Answer 1

I can't see the rectangle image clearly from your message. Could you either

- upload the picture of the graph, or
- tell me the coordinates of A, B, C, D (or at least A and C and whether sides are horizontal/vertical)?

Meanwhile, here is the method (and an example) so you can finish it immediately once you supply or read the coordinates:

1. Find the side lengths.
- If AB is horizontal, length AB = |xB − xA|. If vertical, AB = |yB − yA|.
- CD has the same length as AB because opposite sides of a rectangle are equal.

2. Find new coordinates of C when you double each side while fixing A.
- Let vector AC = (xC − xA, yC − yA). Doubling each side from A means the new C (call it C') is
C' = A + 2·(AC) = (xA + 2(xC − xA), yA + 2(yC − yA)).
- Equivalently, C' = (2xC − xA, 2yC − yA).

Example (illustration):
- Suppose A = (2,1), B = (8,1), C = (8,5), D = (2,5).
- AB = |8 − 2| = 6, so AB and CD are each 6 units long.
- AC = (8 − 2, 5 − 1) = (6,4). Doubling gives 2·AC = (12,8).
- New C' = A + 2·AC = (2+12, 1+8) = (14,9). (You can also compute C' = (2·8 − 2, 2·5 − 1) = (14,9).)

Give me the actual coordinates (or the image) and I will compute the exact numeric answers for your rectangle.