Level 2 · Intermediate ← Back to lesson

Distance and Midpoint: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

For $A$ at $(-6,1)$ and $B$ at $(2,7)$ , find the distance from $A$ to the midpoint of $AB$ .

Answer choices for question 1 A $10$ units B $7$ units C $5$ units D $25$ units
2

The midpoint of $AB$ is $(-3/2,2)$ , and $B=(4,-3)$ . Find $A$ .

Answer choices for question 2 A $(-7,7)$ B $(-11/2,5)$ C $(1,1)$ D $(-7,1)$
3

For $A$ at $(-5,2)$ and $B$ at $(1,-2)$ , what is the exact length $AB$ in simplest radical form?

Answer choices for question 3 A $\sqrt{40}$ B $10$ C $4\sqrt{13}$ D $2\sqrt{13}$
4

A is at $(-2,1)$ . Point B is at $(t,4)$ , and $AB$ is 5 units. Which list gives all possible values of $t$ ?

Answer choices for question 4 A $-4$ and $4$ B $-6$ and $2$ C $2$ only D $-7$ and $3$
5

The midpoint of $AB$ is $(2,3)$ . Both endpoints have x-coordinate 2, and $A$ has y-coordinate $-4$ . What is $AB$ ?

Answer choices for question 5 A $7$ units B $10$ units C $3$ units D $14$ units
6

Segments $AB$ and $CD$ have endpoints $A$ at $(-4,-2)$ , $B$ at $(2,4)$ , $C$ at $(-2,4)$ , and $D$ at $(4,-2)$ . How are their midpoints positioned?

Answer choices for question 6 A They have the same midpoint. B The midpoint of CD is 2 units above the midpoint of AB. C The midpoint of CD is 2 units right of the midpoint of AB. D The midpoint of CD is 2 units left of the midpoint of AB.
7

For $A$ at $(-1,0)$ , $B$ at $(3,2)$ , and $P$ at $(1,1)$ , which statement confirms that P is the midpoint of AB?

Answer choices for question 7 A P has both coordinate averages and lies halfway along AB. B P has an x-coordinate between those of A and B, which alone is sufficient. C P has the same y-coordinate as A. D P is 1 unit from both endpoints.
8

Triangle ABC has squared side lengths 20 for AB, 45 for AC, and 29 for BC. Under the order ABC to DEF, which data establish congruence?

Answer choices for question 8 A
$DE^2=20$

$DF^2=29$

$EF^2=45$
B
$DE^2=20$

$DF^2=45$

$EF^2=29$
C
$DE^2=45$

$DF^2=20$

$EF^2=29$
D
$DE^2=20$

$DF^2=45$

$EF^2=30$
9

A straight cable joins map points $(-2,-1)$ and $(4,4)$ . Each coordinate unit represents 3 meters. What exact cable length is needed?

Answer choices for question 9 A $\sqrt{61}$ meters B $33$ meters C $3\sqrt{61}$ meters D $9\sqrt{61}$ meters
10

A segment has endpoints $(-5,3)$ and $(1,-1)$ . The second endpoint moves to $(5,-3)$ while the first stays fixed. What is the new midpoint?

Answer choices for question 10 A $(-2,1)$ B $(0,0)$ C $(2,-1)$ D $(5,-3)$
11

For $A$ at $(-3,2)$ , $B$ at $(4,6)$ , and $C$ at $(5,-1)$ , which segment is longer, AB or AC?

Answer choices for question 11 A AB, because its squared length is 65 rather than 73. B They have equal lengths. C AB, because its vertical gap is greater. D AC, because its squared length is 73 rather than 65.
12

With $A$ at $(1,-3)$ and $B$ at $(t,2)$ , for which prescribed length is there exactly one possible endpoint B?

Answer choices for question 12 A $5$ units B $4$ units C $6$ units D $7$ units

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