MCAS Math Camp Practice

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape. It is defined by a scale factor and a center of dilation.

Front

What is the scale factor in dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you perform a dilation on a triangle in the coordinate plane?

Back

To dilate a triangle, multiply the coordinates of each vertex by the scale factor. For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), and the scale factor is k, the new vertices will be (kx1, ky1), (kx2, ky2), (kx3, ky3).

Front

What is the origin in the coordinate plane?

Back

The origin is the point (0, 0) in the coordinate plane where the x-axis and y-axis intersect.

Front

What does it mean for a triangle to be dilated with respect to the origin?

Back

Dilation with respect to the origin means that the center of dilation is at the origin (0, 0), and all points of the triangle are moved away from or towards the origin based on the scale factor.

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the new coordinates after a dilation by a scale factor of 2?

Back

The new coordinates will be (4, 6), (8, 10), and (12, 14) after multiplying each coordinate by 2.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

How does dilation affect the area of a triangle?

Back

When a triangle is dilated by a scale factor of k, the area of the triangle is multiplied by k^2.

Front

What is a coordinate plane?

Back

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis). Each point on the plane is defined by an ordered pair of numbers (x, y).

Front

What is the difference between enlargement and reduction in dilation?

Back

Enlargement occurs when the scale factor is greater than 1, making the figure larger. Reduction occurs when the scale factor is between 0 and 1, making the figure smaller.