Dilations and Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is a scale factor in dilations?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. It determines how much larger or smaller the image will be compared to the original figure.

Front

If a figure is dilated by a scale factor of 1/3, what happens to its size?

Back

The figure will be reduced to one-third of its original size.

Front

If a figure is dilated by a scale factor of 2, what happens to its size?

Back

The figure will be enlarged to twice its original size.

Front

What is the relationship between the lengths of corresponding sides of similar figures?

Back

The lengths of corresponding sides of similar figures are proportional to the scale factor.

Front

If a line segment has a length of 12 units and after a dilation the image length is 4 units, what is the scale factor?

Back

1/3

Front

How do you determine the scale factor when comparing two similar figures?

Back

The scale factor can be determined by dividing the length of a side of the larger figure by the length of the corresponding side of the smaller figure.