Question

QR is a diameter and Q(1,8) and C(3.5,2) are points on a coordinate plane. Find and state the coordinates of Point R

Answer 1

Answer:

The coordinates of point R are $R(x,y) = (6, -4)$.

Step-by-step explanation:

From Geometry we understand that magnitude of Diameter is twice the magnitude of Radius. Vectorially speaking, both radius and diameter are collinear. That is:

$\overrightarrow{QR} = 2\cdot \overrightarrow{QC}$ (1)

Where:

$\overrightarrow{QC}$ - Vector radius.

$\overrightarrow{QR}$ - Vector diameter.

If we know that $Q(x,y) = (1,8)$ and $C(x,y) = (3.5,2)$, then coordinates of point R are, respectively:

$R(x,y) -Q(x,y) = 2\cdot C(x,y)-2\cdot Q(x,y)$

$R(x,y) = 2\cdot C(x,y) -Q(x,y)$

$R(x,y) = 2\cdot (3.5, 2) - (1,8)$

$R(x,y) = (6, -4)$

The coordinates of point R are $R(x,y) = (6, -4)$.