Dilate rectangle
1 answer:
Answer:
The coordinates of the points of the rectangle A'B'C'D' are;
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = (2, -1)
Step-by-step explanation:
Placing the point P as the origin of the chart, we have;
The coordinates of the points are given as follows;
The coordinates of the point B = (-4, 2)
The coordinates of the point C = (4, 2)
The coordinates of the point A = (-4, -2)
The coordinates of the point D = (4, -2)
Given that the sides are parallel to the axis, we have;
The length of the segment AB = 2 - (-2) = 4
The length of the segment BC = 4 - (-4) = 8
The length of the segment CD = 2 - (-2) = 4
The length of the segment AD = 4 - (-4) = 8
Therefore, a dilation by 1/2 will give;
The length of the segment A'B' = AB/2 = 4/2 = 2
The length of the segment B'C' = BC/2 = 8/2 = 4
The length of the segment C'D' = CD/2 = 4/2 = 2
The length of the segment A'D' = AD/2 = 8/2 = 4
The coordinates of the point A' = The coordinates of the point A/2 = (-4, -2)/2 = (-2, -1)
The coordinates of the point A' = (-2, -1)
The coordinates of the point B' = The coordinates of the point B/2 = (-4, 2)/2 = (-2, 1)
The coordinates of the point B' = (-2, 1)
The coordinates of the point C' = The coordinates of the point C/2 = (4, 2)/2 = (2, 1)
The coordinates of the point C' = (2, 1)
The coordinates of the point D' = The coordinates of the point D/2 = (4, -2)/2 = (2, -1)
The coordinates of the point D' = (2, -1).
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<h3>Answer: Check out the diagram below.</h3>
Explanation:
Use your straightedge to extend segment AB into ray AB. This means you'll have it start at A and go on forever through B. Repeat these steps to turn segment AC into ray AC.
The two rays join at the vertex angle A. Point A is the center of the universe so to speak because it's the center of dilation. We consider it an invariant point that doesn't move. Everything else will move. In this case, everything will move twice as much compared to as before.
Use your compass to measure the width of AB. We don't need the actual number. We just need the compass to be as wide from A to B. Keep your compass at this width and move the non-pencil part to point B. Then mark a small arc along ray AB. What we've just done is constructed a congruent copy of segment AB. In other words, we've just double AB into AB'. This means the arc marking places point B' as the diagram indicates.
The same set of steps will have us construct point C' as well. AC doubles to AC'
Once we determine the locations of B' and C', we can then form triangle A'B'C' which is an enlarged copy of triangle ABC. Each side of the larger triangle has side lengths twice as long.
Note: Points A and A' occupy the same exact location. As mentioned earlier, point A doesn't move.