Question

Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the point (4, −2) .



Use the polygon tool to graph the dilated figure.

Answer 1

Answer:

The coordinates for the answer are A (2,0), B (3, 2), and C (5,0).

Step-by-step explanation: We are asked to graph the image of the triangle after dilating it with a scale factor of 1/3 centered at the point (4,-2). This means that we have to find the distance from (4,-2) to each set of coordinates, and then multiply those numbers by a scale factor of 1/3.

So let's start with point A, whose original coordinates are (-2,4).  To find the distance between point A and the scale factor centered at point (4,-2), we have to just count the horizontal (left/right) distance and the vertical (up/down) distance.  Now it is important to note, that you do not count the scale factor as a point of distance. With this in mind, by looking at the graph, we can see that in order for the scale factor to reach Point A, it has to move to the left 6 and up 6. Now that we know the distance between the two points, we can take the scale factor, 1/3, and multiply that to our distance. So 6 times 1/3 to the left, and 6 times 1/3 up= 2 to the left, and 2 up. So from the scale factor centered at (4,-2), we move 2 to the left and 2 up to get our new point A, which has coordinates of (2,0).

Onto the next point, B, whose original coordinates are (1,10).  To find the distance between point B and the scale factor centered at point (4,-2), we have to do the same thing and count the horizontal (left/right) distance and the vertical (up/down) distance.  Now it is important to note, that you do not count the scale factor as a point of distance. With this in mind, by looking at the graph, we can see that in order for the scale factor to reach Point B, it has to move to the left 3 and up 12. Now that we know the distance between the two points, we can take the scale factor, 1/3, and multiply that to our distance. So 3 times 1/3 to the left, and 12 times 1/3 up= 1 to the left, and 4 up. So from the scale factor centered at (4,-2), we move 1 to the left and 4 up to get our new point B, which has coordinates of (3,2).

Lastly, point C, whose original coordinates are (7,4).  To find the distance between point C and the scale factor centered at point (4,-2), we have to do the same thing and count the horizontal (left/right) distance and the vertical (up/down) distance.  Now it is important to note, that you do not count the scale factor as a point of distance. With this in mind, by looking at the graph, we can see that in order for the scale factor to reach Point C, it has to move to the right 3 and up 6. Now that we know the distance between the two points, we can take the scale factor, 1/3, and multiply that to our distance. So 3 times 1/3 to the left, and 6 times 1/3 up= 1 to the left, and 2 up. So from the scale factor centered at (4,-2), we move 1 to the left and 2 up to get our new point C, which has coordinates of (5,0).

Please let me know if you have any questions and/or confused about any of the steps! (I was taking the quiz when I looked this exact question up for the answer, and saw no response. So, I finished the quiz, had gotten the answer right, and decided to post it here for anyone else)

Answer 2

The needed coordinates are (3,2), (2,0), (5,0).

The graph of dilated image is shown below.

Given coordinates of the triangle : (1,10), (7,4), (-2,4)

Dilation's scale factor: 1/3

Dilation's center point (4,-2)

To find the dilation from point (4,-2), we measure the distances of old triangle's vertices and scale it by given scale factors.

Scaling line segment [(4,-2), (1,10)]  0.333.. times result in line segment [(4,-2), (3,2)].

We get such result by:

$D_x = 4\\D_y = -2\\P_x = 1\\P_y = 10\\New_x =D_x - (D_x - P_x) \times \dfrac{1}{3} = 4 - 1 = 3\\\\New_y =D_y - (D_y - P_y) \times \dfrac{1}{3} = 2$

Similarly calculating the new coordinates, we get following results.

Scaling line segment [(4,-2), (7,4)]  0.333.. times result in line segment [(4,-2), (5,0)].

Scaling line segment [(4,-2), (-2,4)]  0.333.. times result in line segment [(4,-2), (2,0)].

Thus, the needed coordinates are (3,2), (2,0), (5,0).

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