Question

PLEASE HELP!!!
△AOC~△BOD. Identify the coordinates of D and the scale factor.


A.) D (0, −7 1/12); 2/5


B.) D (0, −1 1/5); 5/2


C.) D (0, −7 1/2); 5/2


D.) D (0, −1 1/5); 2/5

Answer 1

The coordinate of D is $(0, -1\frac{1}{5})$ and the scale factor is 2/5.

The correct option is D.) D (0, −1 1/5); 2/5

To determine the coordinates of D, we will first determine the length of /OD/

Consider △AOC and △BOD. They are similar triangles.

From the diagram, we can determine the lengths of the sides of each triangle /OB/ = 2 units, /OA/ = 5 units, /OC/ = 3 units and /OD/ is unknown

Since △AOC is similar △BOD, then we can write that

$\frac{/OB/}{/OA/} = \frac{/OD/}{/OC/}$

∴ $\frac{2}{5} = \frac{/OD/}{3}$

$/OD/ \times 5 = 2 \times 3$

$/OD/ \times 5 = 6$

Then,

$/OD/ = \frac{6}{5}$

∴ $/OD/ = 1\frac{1}{5}$

Hence, the coordinate of D is $(0, -1\frac{1}{5})$ since D is on the negative side of the y-axis.

For the scale factor,

Scale factor = $\frac{/OB/}{/OA/}$

Scale factor = $\frac{2}{5}$

Hence, the scale factor is 2/5

The correct option is D.) D (0, −1 1/5); 2/5

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