Question

1. the solid - line figure is a dilation of the dashed - line figure. the labeled point is the center of dilation. tell whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation.
2. △abc is a dilation image of △abc. the scale factor for the dilation is 1.25. is the dilation an enlargement or a reduction?
3. △pqr is a dilation image of △pqr. the scale factor for the dilation is 0.12. is the dilation an enlargement or a reduction?

a dilation has center (0, 0). find the image of each point for the given scale factor.

1. x(3, 4); d_7(x)
2. q(0, 4); d_3.4(q)
3. s(5, - 6); d_(1/3)(s)
4. p(-3, 5); d_2.5(p)
5. t(-2, -1); d_4(t)
6. m(2, 2); d_5(m)
7. graph pentagon abcde and its image abcde for a dilation with center (0, 0) and a scale factor of 1.5. the vertices of abcde are: a(0, 3), b(3, 3), c(3, 0), d(0, - 3), e(-1, 0).
8. graph pentagon penta and its image d_0.5(penta)=penta. the vertices of penta are: p(0, 4), e(6, 6), n(4, 0), t(0, - 4), a(-2, 0).

Explanation:

8.

Step1: Determine type of dilation

If the scale - factor \(k>1\), it's an enlargement; if \(0 < k<1\), it's a reduction.

Step2: Measure lengths

Count the distances from the center of dilation to corresponding points on the solid - line and dashed - line figures. Let's assume we find that the ratio of the distance from the center of dilation to a point on the solid - line figure to the distance from the center of dilation to the corresponding point on the dashed - line figure is \(k\). Suppose \(k = 2\) (by measurement). Since \(k = 2>1\), it's an enlargement.

The scale factor \(k = 1.25\). Since \(1.25>1\), if a dilation has a scale factor \(k>1\), the image is larger than the pre - image.

The scale factor \(k = 0.12\). Since \(0<0.12 < 1\), when the scale factor of a dilation satisfies \(0 < k<1\), the image is smaller than the pre - image.

Answer:

Enlargement, scale factor \(2\)

9.