2 years ago

Describe a set of transformations that would map Triangle FGH onto Triangle F’G’H’

1 answer:

6 0

The translations would be this

1) reflection over the x-axis
2) translation of (-6,0)

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nlexa [21]

$$ PS = \frac{4}{3} x$

Solution:

Given PRQ is a triangle.

ST is a line parallel to RQ.

$$PT = x, \ PQ = 3x, \ SR=\frac{8}{3}x$

$TQ=PQ-PT$

$TQ=3x -x=2x$

Triangle proportionality theorem,

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

$$\frac{PS}{SR} =\frac{PT}{TQ}$

$$\frac{PS}{\frac{8}{3} x} =\frac{x}{2x}$

Do cross multiplication, we get

$$ PS \times 2x=x \times \frac{8}{3} x$

Divide by 2x on both sides, we get

$$ PS = \frac{4}{3} x$

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3 years ago