Question

R(3, 8) is dilated by a factor of 5, centered at (2, 10). Write the coordinates of R’.

Answer 1

Answer:

The coordinates of R' are $R'(x,y) = (8,-2)$.

Step-by-step explanation:

According to Linear Algebra, dilation consist in expanding a given vector with  respect to one of its endpoints by a scalar. That is:

$R'(x, y) = C(x,y) + k\cdot [R(x,y)-C(x,y)]$ (Eq. 1)

Where:

$R(x, y)$ - Original location with respect to origin, dimensionless.

$C(x,y)$ - Point of reference with respect to origin, dimensionless.

$k$ - Dilation factor, dimensionless.

$R'(x, y)$ - Dilated point with respect to origin, dimensionless.

If we know that $R(x,y) = (3,8)$, $C(x,y) = (2,10)$ and $k = 5$, then the dilated point is:

$R'(x,y) = (3,8) +5\cdot [(3,8)-(2,10)]$

$R'(x,y) = (3,8)+5\cdot (1,-2)$

$R'(x,y) = (8,-2)$

The coordinates of R' are $R'(x,y) = (8,-2)$.