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

Answer:

Q(20,10)

Step-by-step explanation:

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

$\overrightarrow {PT}=\dfrac{3}{10}\overrightarrow {PQ}.$

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,

$(6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).$