Question

. Given PQ and point ???? that lies on PQ such that point ???? lies 7 / 9 of the length of PQ from point P along PQ:

a. Sketch the situation described.
b. Is point ???? closer to P or closer to ????, and how do you know?
c. Use the given information to determine the following ratios:
i. PR: PQ
ii. ????Q: PQ
iii. PR: ????Q
iv. ????Q: PR
d. If the coordinates of point P are (0, 0) and the coordinates of point ???? are (14, 21), what are the coordinates
of point ?????

Answer 1

Point R is closer to Q.

Explanation:

Correct Question Statement:

Given PQ and point R that lies on PQ such that point ???? lies 7 / 9 of the length of PQ from point P along PQ:

a. Sketch the situation described.

b. Is point R closer to P or closer to R, and how do you know?

c. Use the given information to determine the following ratios:

i. PR: PQ

ii. RQ: PQ

iii. PR: RQ

iv. RQ: PR

d. If the coordinates of point P are (0, 0) and the coordinates of point R are (14, 21), what are the coordinates

of point Q.

ANSWER

a. PQ is the line as shown below:

P_______R__Q

Point R lies at 7/9 means if PQ is divided in 9 parts then R lies at 7th place.

b. point R is closer to Q as shown above.

c. Ratios:

i. PR:PQ = 7:9.

ii. RQ:PQ = 2:9

iii. PR:RQ = 7:2.

iv. RQ:PR = 2:7.

d. Suppose coordinates of Q are (x,y)

7/9 of x is 14 → (7/9)*x = 14 → x =
`(14*9)/(7)` = 18

7/9 of y is 21 → (7/9)*y =21 → y =
`(21*9)/(7)` =27

Thus, Q(18,27) are required coordinates.