Q:

# Consider line segment AB whose endpoints are (1, 4) and (4, 8). If this segment is dilated by a scale factor of 4 centered at the origin, find the length of the new segment, A’B’.A. 4 B. 5 C.20 D. 400

Accepted Solution

A:
Answer:The length of the new segments A'B' is 20 units ⇒ answer CStep-by-step explanation:* Lets revise the dilation- A dilation is a transformation that changes the size of a figure.  - It can become larger or smaller, but the shape of the  figure does  not change.  - The scale factor, measures how much larger or smaller the image  will be- If the scale factor greater than 1, then the image will be larger- If the scale factor between 0 and 1, then the image will be smaller* Lets solve the problem- line segment AB whose endpoints are (1, 4) and (4, 8) is dilated by  a scale factor of 4 and centered at the origin∵ The scale factor is 4 and it is greater than 1- The length of the image of line segment AB will enlarged by the    scale factor 4∴ A'B' = 4 AB* Lets find the length of AB by using the rule of the distance∵ $$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$$∵ A = $$(x_{1},y_{1})$$ and B = $$(x_{2},y_{2})$$∵ A = (1 , 4) and B = (4 , 8)∴ $$(x_{1},y_{1})=(1 , 4)$$ and $$(x_{2},y_{2})=(4 , 8)$$∵ AB = $$\sqrt{(4-1)^{2}+(8-4)^{2}}=5$$∴ AB = 5 units∵ A'B' = 4 AB∴ A'B' = 4 × 5 = 20∴ The length of the new segments A'B' is 20 units