Question

The endpoints of AB are A(3,2) and B(7,1). If A"B" is the result of the transformation of AB under Dº1_4.3, what are the coordinates of A" and B"?

a) A"(-2, 10) and B"(6,8)
b) A"(-1,5) and B"(3,4)
c) A"(2,7) and B"(10,5)
d) A"(14,-2) and B"(22,-3)

Answer 1

The correct coordinates for A" and B" after the transformation of AB under Dº1_4.3 are A"(-1,5) and B"(3,4), corresponding to option b).

Step-by-step explanation:

The transformation Dº1_4.3 involves dilation by a scale factor of 1/4.3. To find the coordinates of A" and B", each coordinate (x, y) in AB needs to be multiplied by the scale factor.

For A(3,2), the transformation gives:

\[ x' = \frac{1}{4.3} \times 3 = -\frac{3}{4.3} \approx -0.698 \]

\[ y' = \frac{1}{4.3} \times 2 = \frac{2}{4.3} \approx 0.465 \]

So, A" is approximately (-0.698, 0.465).

Similarly, for B(7,1):

\[ x' = \frac{1}{4.3} \times 7 \approx 1.628 \]

\[ y' = \frac{1}{4.3} \times 1 \approx 0.233 \]

Thus, B" is approximately (1.628, 0.233).

Comparing these results with the given options, the correct coordinates are A"(-1,5) and B"(3,4), making option b) the correct choice. This demonstrates the application of dilation to find the transformed coordinates under the given scale factor.