Question

Find the point R that breaks the directed segmentre in a ratio of 1:3. given point P(-4,5) and point Q(4,1).

Answer 1

Find the point R that breaks the directed segmentre in a ratio of 1:3. given point P(-4,5) and point Q(4,1).​

we have that

PR/RQ=1/3

or

PR/PQ=1/(1+3) ------> PR/PQ=1/4

step 1

Find the horizontal distance between P and Q (PQx)

PQx=4-(-4)=8 units

we hve

PRx/PQx=1/4

solve for PRx (horizontal distance between P and R)

PRx=PQx/4 -------> PRx=8/4=2

Find the x-coordinate of point R (Rx)

Rx=Px+PRx -----> Rx=-4+2=-2

the horizontal coordinate of R is -2

step 2

Find the vertical distance between P and Q (PQy)

PQy=5-1=4 units

we have

PRy/PQy=1/4

solve for PRy (vertical distance between P and R)

PRy=PQy/4 -----> PRy=4/4=1

Find the y-coordinate of point R (Ry)

Ry=Py-PRy ------> Ry=5-1=4

the y-coordinate of R is 4

therefore

the coordinates of point R are (-2,4)