Question

Suppose segment PQ has one endpoint at P (0,0). If T (6,3) is a point 3/10 of the way from P to Q, find the coordinates of Q.

Answer 1

Q(20,10)

Explanation:

If point T (6,3) is a point 3/10 of the way from P(0,0) to Q(x,y), then

`\overrightarrow {PT}=(3)/(10)\overrightarrow {PQ}.`

Find the coordinates of the vectors
`\overrightarrow {PT},\ \overrightarrow {PQ}:`

`\overrightarrow {PT}=(6-0,3-0)=(6,3);\\ \\\overrightarrow {PQ}=(x-0,y-0)=(x,y).`

Thus,

`(6,3)=(3)/(10)(x,y),\\ \\(x,y)=(10)/(3)(6,3)=(20,10).`