(A) what does the scale factor tell you about two similar shapes? (B) How does the coordinate rule for making two similar shapes relate to the scale factor?
What does the scale factor tell you about two similar shapes?
A) The scale factor tells you the ratio of the corresponding sides of two similar shapes. In other words, it describes how much larger or smaller one shape is compared to the other. It can be thought of as a multiplier that scales the dimensions of one shape to match the dimensions of the other.
For example, if the scale factor is 2, it means that the lengths of corresponding sides of the two shapes are in a 1:2 ratio. This implies that one shape is twice as large as the other in all dimensions.
B) The coordinate rule for making two similar shapes states that each coordinate of the original shape should be multiplied by the scale factor to obtain the corresponding coordinate of the new shape. This rule ensures that the relative positions and proportions of the points on the shape are maintained while scaling.
To apply the coordinate rule, you multiply the x-coordinate and the y-coordinate of each point of the original shape by the scale factor. This will give you the corresponding coordinates of the points in the new shape.
For example, let's say we have a point in the original shape with coordinates (x, y), and the scale factor is k. Applying the coordinate rule, the coordinates of the corresponding point in the new shape will be (k * x, k * y).
By using this rule for each point, you can create a new, similar shape that is scaled proportionally to the original shape.