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Each vertex of a quadrilateral is dilated by a factor of 1/2 about the point P (-3,7). What will be the effect on the perimeter of the resulting figure.

Each Vertex Of A Quadrilateral Is Dilated By A Factor Of 12 About The Point P 37 What Will Be The Effect On The Perimeter Of The Resulting Figure class=

Sagot :

Note that the perimeter of any quadrilateral is the sum of its sides.

[tex]P=\sum ^n_{i\mathop=1}a_i[/tex]

So it is always proportional to the length of any side,

[tex]P\propto a_i[/tex]

Note that the dilation either stretches of compresses the sides.

For the factor 1/2, each side of the quadrilateral will get multiplied by 1/2, which simply means that the sides will get halved.

So the new perimeter is given by,

[tex]P^{\prime}=\sum ^n_{i=1}(\frac{1}{2}a_i)=\frac{1}{2}\sum ^n_{i=1}(a_i)=\frac{1}{2}P[/tex]

Thus, the perimeter will also get halved due to the dilation.

Therefore, option A is the correct choice.

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