Question

Consider AB in the coordinate plane below. What will be the y-coordinate of B’ if AB is dilated by a factor of 2/5, centered at the origin?

Answer 1

4/5

Explanation:

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Answer 2

`\boxed{(4)/(5)}`

Explanation:

Dilation is when you stretch something by the same amount in two perpendicular directions. In other words, dilation changes size, not overall shape. Dilation factors greater than one makes the shape greater while dilation factors less than one makes the shape smaller. The general form of a dilation is shown in the figure below. In this problem, we must find the y-coordinate of B' if AB is dilated by a factor 2/5. Since 2/5 is less than one, then the dilated line formed will be shorter than the one formed by AB. Hence, to dilate B by a factor of 2/5, centered at the origin, we just multiply both x- and y- coordinate by 2/5, accordingly:

`B(10,2) \rightarrow B'(10* (2)/(5), 2* (2)/(5)) \therefore B'(4,(4)/(5))`

Finally, the y-coordinate of B’ is:

`\boxed{(4)/(5)}`