Question

On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r?

Answer 1

The coordinates of point r(-8,0).

What is midpoint formula in coordinate geometry?

The coordinates of the point r(x,y) which divides the line segment joining the points p($x_{1}$,$y_{1}$) and q($x_{2}$,$y_{2}$) internally in the ratio :$m_{1}$$m_{2}$ are

$\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)$

Given that,

Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5

$m_{1}$ = 3 and $m_{2}$ = 5

By using the midpoint formula

$\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)$

$\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)$

$\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)$

$\left(-8 ,0\Rifgt)$

Hence, The coordinates of point r(-8,0).

To learn more about midpoint formula from the given link:

brainly.com/question/4429656

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