Question

Suppose P is a point not on line segment WX . Let YZ be the dilation of line segment WX using P as the center with scale factor 2. Experiment using a circular grid to make predictions about whether each of the following statements must be true, might be true, or must be false.YZ is twice as long WX. YZ is five units longer than WX.The point P is on YZ.YZ and WX intersect.

Answer 1

To imagine the situation, draw a segment WX and a point P outside it:

Draw the dilation by a factor of 2 using P as the center of the dilation:

Using a circular grid, the diagram may look something like this:

Analyze each statement to make predictions.

"YZ is twice as long as WX"

Since the dilation has a scale factor of 2, this statement must be true.

"YZ is five units longer than WX"

Since we do not know the length of WX, this statement may be true if WX=5. This way, YZ would be equal to 10. But this is not necessarily true. Therefore, this statement might be true.

"The point P is on YZ"

Since P is outside WX, there is no way that P is on YZ. Therefore, this statement must be false.

"YZ and WX intersect"

From the diagram, it looks like YZ and WX are parallel. Therefore, this statement must be false.