Slope & Dilations

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change 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 the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a scale factor.

Front

What is a scale factor in dilations?

Back

The scale factor is the ratio of the length of a side of the image to the length of the corresponding side of the original figure.

Front

If point A (4, 6) is dilated to point A' (8, 12), what is the scale factor?

Back

The scale factor is 2.

Front

If point B (2, 3) is dilated to point B' (1, 1.5), what is the scale factor?

Back

The scale factor is 0.5.