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

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

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)`.