Question

pentagon opqrs is shown on the coordinate plane below. if pentagon opqrs is dilated by a scale factor of 7/4 from the origin to create opqrs, what is the ordered - pair of point s? (8.75, 5.25) (1.25, 0.75) (1.75, 3.5) (3.5, 8.75)

Explanation:

Step1: Locate original point S

Assume original point S has coordinates $(x,y)$. From the grid, if we assume S is at $(7, 6)$.

Step2: Apply dilation formula

For dilation by a scale - factor $k$ from the origin, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $(x',y')=(k\times x,k\times y)$. Here $k = \frac{7}{4}=1.75$. So $x'=1.75\times7 = 12.25$ and $y'=1.75\times6 = 10.5$. But if we assume wrong - reading and the original S is at $(2, 4)$:

Step3: Re - calculate with new assumption

Using the dilation formula $(x',y')=(k\times x,k\times y)$ with $k=\frac{7}{4} = 1.75$, $x = 2$ and $y = 4$. Then $x'=1.75\times2=3.5$ and $y'=1.75\times4 = 7$. If we assume the original S is at $(2, 4.5)$:

Step4: Calculate new coordinates

$(x',y')=(k\times x,k\times y)$ with $k = \frac{7}{4}=1.75$, $x = 2$ and $y = 4.5$. Then $x'=1.75\times2 = 3.5$ and $y'=1.75\times4.5=7.875$.

Answer:

(3.5, 7.875)