Partitioning a Line Segment Review

Find the coordinates of point  $P$  that lies on  $\overline{MQ}$  ,  $M\left(-9,-5\right)$  ,  $Q\left(3,5\right)$  and partitions the segment at a ratio of 2:5.

•  $P\left(-3,0\right)$  

•   $P\left(\frac{-39}{7},\frac{-15}{7}\right)$  

•  $P\left(-6,-5\right)$  

•  $P\left(-5,-6\right)$  

Tags

CCSS.HSG.GPE.B.6

Point A has coordinates  $\left(-9,-7\right)$   and point B has coordiantes  $\left(3,8\right)$ . Find the coordinates of point  $P$  that partion  $\overline{AB}$  in the ratio 2:1. 

•  $P\left(3,-0.5\right)$  

•  $P\left(-6,-7.5\right)$  

•  $P\left(-3,0.5\right)$  

•  $P\left(-1,3\right)$  

Tags

CCSS.HSG.GPE.B.6

Point  $P$  partitions  $\overline{AB}$   with  $AP:AB=\frac{2}{5}$ . Find the coordinates of  $B$  if  $A\left(5,5\right)$  and  $P\left(-2,-5\right)$ .

•  $B\left(3,\frac{15}{7}\right)$  

•  $B\left(-19.5,-30\right)$  

•  $B\left(-12.5,-20\right)$  

•  $B\left(2.2,1\right)$  

Tags

CCSS.HSG.GPE.B.6

Point  $K$  partitions  $\overline{JL}$  with  $JK:KL=\frac{3}{4}$ . What is the value of k?

•  $\frac{3}{4}$  

•  $-\frac{3}{4}$  

•  $\frac{3}{12}$  

•  $\frac{3}{7}$  

Tags

CCSS.HSG.GPE.B.6

Point  $K$ partitions  $\overline{JL}$ with  $JK:JL=\frac{4}{5}$ . What is the value of k?

•  $\frac{4}{5}$  

•  $-\frac{4}{5}$  

•  $\frac{4}{20}$  

•  $\frac{4}{9}$  

Tags

CCSS.7.EE.B.3

How do you find the x-coordinate of a partition point?

• $x_p=x_1-k\left(x_2-x_1\right)$

• $x_p=x_2-k\left(x_2+x_1\right)$

• $x_p=x_2+k\left(x_2+x_1\right)$

• $x_p=x_1+k\left(x_2-x_1\right)$

Tags

CCSS.HSG.GPE.B.6

How do you find the y-coordinate of the partition point?

• $y_p=y_1-k\left(y_2-y_1\right)$

• $y_p=y_1+k\left(y_2-y_1\right)$

• $y_p=y_1+k\left(y_2+y_1\right)$

• $y_p=y_2-k\left(y_2-y_1\right)$

Tags

CCSS.HSG.GPE.B.6

Find the coordinates of point  $P$  that lies on  $\overline{MQ}$  ,  $M\left(-3,-2\right)$  ,  $Q\left(2,3\right)$  and partitions the segment at  $MP:PQ=\frac{2}{3}$  .

•  $P\left(-1,0\right)$  

•   $P\left(0,1\right)$  

•  $P\left(\frac{1}{3},\frac{4}{3}\right)$  

•  $P\left(-\frac{17}{5},-\frac{8}{5}\right)$  

Tags

CCSS.HSG.GPE.B.6