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Circle $B$ with a radius of $5$ units is shown on a coordinate grid. Circle $B$ is dilated by a scale factor of $\frac{7}{5}$ , centered at the origin, to map to Circle $M$ . $\newline$ Complete the statement.

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Convert equations of circles from general to standard form

Full solution

Q. Circle

B

with a radius of

5

units is shown on a coordinate grid. Circle

B

is dilated by a scale factor of

\frac{7}{5}

, centered at the origin, to map to Circle

M

.

\newline

Complete the statement.

Understand effect of dilation: Understand the effect of dilation on the radius. Dilation of a circle by a scale factor will multiply the radius of the original circle by that scale factor to get the new radius.
Calculate new radius: Calculate the new radius of Circle M. $\newline$ The original radius of Circle B is $5$ units. The scale factor for the dilation is $\frac{7}{5}$ . To find the new radius, multiply the original radius by the scale factor: $\newline$ New radius $=$ Original radius $\times$ Scale factor $\newline$ New radius $= 5 \times \left(\frac{7}{5}\right)$
Perform multiplication: Perform the multiplication to find the new radius. $\newline$ New radius = $5 \times (7/5)$ $\newline$ New radius = $(5/1) \times (7/5)$ $\newline$ New radius = $(5 \times 7) / (1 \times 5)$ $\newline$ New radius = $35 / 5$ $\newline$ New radius = $7$ units

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