Level 3 · Challenge ← Back to lesson

Partitioning a Segment: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

A is $(-7,5)$ and B is $(14,-9)$ . An internal point P has first coordinate $k$ and second coordinate 1. Find $k$ and $AP:PB$ .

Answer choices for question 1 A $k=1$ , ratio $2:5$ B $k=-1$ , ratio $5:2$ C $k=5$ , ratio $4:3$ D $k=-1$ , ratio $2:5$
2

A is $(-9,4)$ and internal P is $(3,-2)$ . The ordered ratio is $AP:PB=4:3$ . Find B.

Answer choices for question 2 A $(0,-1/2)$ B $(12,-13/2)$ C $(12,-10)$ D $(19,-10)$
3

B is $(10,17)$ and internal P is $(-2,5)$ . If $AP:PB=3:2$ , find A.

Answer choices for question 3 A $(-10,-3)$ B $(-14,-7)$ C $(-20,-13)$ D $(16,23)$
4

A is $(2,-8)$ and B is $(17,12)$ . Which point lies internally on AB?

Answer choices for question 4 A $(8,0)$ B $(8,1)$ C $(11,0)$ D $(18,40/3)$
5

A is $(-4,-7)$ and B is $(11,8)$ . P has $AP:PB=2:3$ and Q has $AQ:QB=4:1$ . What is $PQ:AB$ ?

Answer choices for question 5 A $1:5$ B $2:5$ C $3:5$ D $2:3$
6

A is $(a,2)$ , B is $(12,17)$ , and internal P is $(4,7)$ . If $AP:PB=1:2$ , find $a$ .

Answer choices for question 6 A $-4$ B $2$ C $8$ D $0$
7

A record gives $A(-2,1)$ , $B(b,16)$ and $P(5,8)$ , with $AP:PB=2:3$ . Which statement is correct?

Answer choices for question 7 A No value of b makes the complete record consistent B $b=31/2$ makes the record consistent C $b=15$ makes the record consistent D $b=19$ makes the record consistent
8

A is $(8,12)$ and B is $(-12,-3)$ . A point R is $(0,6)$ . Which pair correctly records its ordered ratios?

Answer choices for question 8 A
$AR:RB=3:2$

$BR:RA=2:3$
B
$AR:RB=2:5$

$BR:RA=3:5$
C
$AR:RB=2:3$

$BR:RA=3:2$
D
$AR:RB=2:3$

$BR:RA=2:3$
9

A is $(9,-14)$ , P is $(9,-2)$ , and B is $(9,b)$ . If P is internal and $AP:PB=3:5$ , find $b$ .

Answer choices for question 9 A $6$ B $10$ C $30$ D $18$
10

On a straight segment AB, P is two sevenths of the way from A and Q is five sevenths of the way from A. What is $AP:PQ:QB$ ?

Answer choices for question 10 A $2:5:2$ B $2:3:5$ C $2:3:2$ D $3:2:3$
11

Let $A(-5,11)$ and $B(16,-3)$ . The point P lies on AB and has first coordinate 4. Which second coordinate and ordered ratio must it have?

Answer choices for question 11 A
$y_P=7$

$AP:PB=3:4$
B
$y_P=5$

$AP:PB=3:4$
C
$y_P=3$

$AP:PB=4:3$
D
$y_P=5$

$AP:PB=3:7$
12

A is $(-15,10)$ , internal P is $(-3,4)$ , and B has second coordinate -8. What is B and the ordered ratio $AP:PB$ ?

Answer choices for question 12 A
$B=(21,-8)$

$AP:PB=1:2$
B
$B=(9,-8)$

$AP:PB=1:2$
C
$B=(21,-8)$

$AP:PB=2:1$
D
$B=(15,-8)$

$AP:PB=1:3$

← Back to lesson