QuestionQuadrilaterals $ABCD$ and $PQRS$ are scaled copies. If $AC = 6$ and $PR = 3$ , find $QS$ .

Studdy Solution

STEP 1

Assumptions1. Quadrilateral $ABCD$ and $QRS$ are similar, meaning they have the same shape but not necessarily the same size. . The corresponding points are to $A$, $Q$ to $B$, $R$ to $C$, and to .
3. The distance from $A$ to $C$ is6 units.
4. The distance from $B$ to is also6 units.
5. The distance from $$ to $R$ is3 units.

STEP 2

In similar figures, the ratio of corresponding sides is constant. This is known as the scale factor. We can find the scale factor by dividing the length of a side in quadrilateral $QRS$ by the corresponding side in quadrilateral $ABCD$ .
$Scale\, factor = \frac{Length\, of\, side\, in\, PQRS}{Length\, of\, corresponding\, side\, in\, ABC}$

STEP 3

Now, plug in the given values for the lengths of corresponding sides to calculate the scale factor.
$Scale\, factor = \frac{PR}{AC} = \frac{3\, units}{6\, units}$

STEP 4

Calculate the scale factor.
$Scale\, factor = \frac{3}{6} =0.$

STEP 5

Now that we have the scale factor, we can find the length of the side $QS$ in quadrilateral $QRS$ by multiplying the length of the corresponding side $BD$ in quadrilateral $ABCD$ by the scale factor.
$QS = BD \\times Scale\, factor$

STEP 6

Plug in the values for the length of side $BD$ and the scale factor to calculate the length of side $QS$ .
$QS =6\, units \\times0.5$

STEP 7

Calculate the length of side $QS$ .
$QS =6 \\times0.5 =3\, units$ The distance from $Q$ to $$ is3 units.

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