Suppose PQ has one endpoint at P(0, 0). If (2,5) is the midpoint of PQ, what are the
coordinates of point Q?

Step-by-step explanation:

The midpoint can be found with the formula.

midpoint = (x1+x2) /2 , (y1 + y2 )/2

 ( x1 , y1), and (x2 , y2 ) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.

P = (0,0)

midpoint = (2,5)

x midpoint = 2 = (0+ x2)/2

×2 = 4

y midpoint = 5 = (y2+0 )/2

10 = y2

so the point Q is (4 , 10)

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}.

PT

10

3

PQ

.

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

PT

,

PQ

:

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

PT

=(6−0,3−0)=(6,3);

PQ

=(x−0,y−0)=(x,y).

Thus,

\begin{gathered}(6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).\end{gathered}

(6,3)=

10

3

(x,y),

(x,y)=

3

10

(6,3)=(20,10).

good job you smart son of a gun you are smarter that einstein. 7

51-50

step-by-step explanation: