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Distance and Midpoint Formula Worksheet - Page 2

Distance and Midpoint Formula Worksheet
  • Page 2
 11.  
Find the distance between A(4, - 5) and B(5, - 8).
a.
4.16 units
b.
3.16 units
c.
6.16 units
d.
5.16 units


Solution:

Distance between two points d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

d = (5 - 4)2+((- 8) - (- 5))2
[Replace (x2, y2) with (5, - 8) and (x1, y1) with (4, - 5).]

d = (1)2+(- 3)2
[Subtract.]

d = 10
[Simplify.]

d 3.16
[Find the positive square root.]

The distance between, A and B is 3.16 units.


Correct answer : (2)
 12.  
The distance between two points (x1, y1) and (x2, y2) is _____.
a.
(x2-x1)+(y2-y1)
b.
(x2-x1)2+(y2-y1)2
c.
x1+y1+x2+y22
d.
| (x2+y2)-(x1+y1) |


Solution:

The distance between two points (x1, y1) and (x2, y2) is (x2-x1)2+(y2-y1)2.


Correct answer : (2)
 13.  
Find the distance between A(- 5, 5) and B(- 7, 3) and round the solution to the nearest tenth.
a.
5.8 units
b.
3.8 units
c.
2.8 units
d.
4.8 units


Solution:

The distance between (x1, y1) and (x2, y2) = d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

d = (- 7 - (- 5))2 +(3 - 5)2
[Replace (x1, y1) with (- 5, 5) and (x2, y2) with (- 7, 3).]

d = (- 2)2+(- 2)2
[Subtract.]

d = 4 + 4 = 8

d 2.828

The distance between A and B is 2.8 units.
[Round the distance to the nearest tenth.]


Correct answer : (3)
 14.  
What is the distance between (x1, y1) and origin?
a.
x12+y12
b.
x12-y12
c.
x1 +y1
d.
x1 -y1


Solution:

The coordinates of origin are (0, 0).

Distance d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

d = (0-x1)2+(0-y1)2
[Replace (x2, y2) with (0, 0).]

d = x12+y12
[Subtract.]

Distance between (x1, y1) and the origin is x12+y12.


Correct answer : (1)
 15.  
Which of the following ordered pairs is at a distance of 2 units from (5, 3)?
a.
(7, 4)
b.
(10, 6)
c.
(8, 7)
d.
(7, 3)


Solution:

Distance, d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

Consider choice A, the distance between (5, 3) and (7, 4).

d = (7 - 5)2+(4 - 3)2 = 5 = 2, which is not true.
[Replace (x1, y1) with (5, 3) and (x2, y2) with (7, 4) and simplify.]

Consider choice B, the distance between (5, 3) and (10, 6).

d = (10 - 5)2+(6 - 3)2 = 34 = 2, which is not true.
[Replace (x1, y1) with (5, 3) and (x2, y2) with (10, 6).]

Consider choice C, the distance between (5, 3) and (8, 7).

d = (8 - 5)2+(7 - 3)2 = 25 = 2, which is not true.
[Replace (x1, y1) with (5, 3) and (x2, y2) with (8, 7).]

Consider choice D, the distance between (5, 3) and (7, 3).

d = (7 - 5)2+(3 - 3)2 = 4 = 2, which is true.
[Replace (x1, y1) with (5, 3) and (x2, y2) with (7, 3).]

Therefore, the point (7, 3) is at a distance of 2 units from (5, 3).


Correct answer : (4)
 16.  
Find the perimeter of the triangle ABC shown in the graph.


a.
26.08 units
b.
30 units
c.
24 units
d.
20.92 units


Solution:

From the figure, A is at (6, - 1), B is at (2, 5) and C is at (- 1, - 1).

Distance d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

AB = (2-6)2+(5-(- 1))2
[Replace (x1, y1) with (6, - 1) and (x2, y2) with (2, 5).]

AB = (- 4)2+62

= 16+36 = 52
[Simplify.]

BC = (- 1-2)2+(- 1-5)2
[Replace (x1, y1) with (2, 5) and (x2, y2) with (- 1, - 1).]

BC = (- 3)2+(- 6)2

= 9+36 = 45
[Simplify.]

CA = (6-(- 1))2+((- 1)-(- 1))2
[Replace (x1, y1) with (- 1, - 1) and (x2, y2) with (6, - 1).]

CA = 72+02

= 49+0 = 49 = 7
[Simplify.]

Perimeter of ΔABC = AB + BC + CA

= 52+45 + 7
[Substitute the values.]

= 7.21 + 6.71 + 7 = 20.92

The perimeter of ΔABC = 20.92 units.


Correct answer : (4)
 17.  
Find the perimeter of quadrilateral ABCD shown in the graph.


a.
13.24 units
b.
22.62 units
c.
24.78 units
d.
19.98 units


Solution:

From the graph, the co-ordinates of A are (7, 7), B are (11, 3), C are (7, - 1) and D are (3, 3).

Distance d = (x2-x1)2+(y2-y1)2
[Use the distance formula.]

AB = (11 - 7)2+(3 - 7)2
[Replace (x1, y1) with (7, 7) and (x2, y2) with (11, 3).]

AB = 42+(- 4)2=16+16=32
[Simplify.]

BC = (7 - 11)2+(- 1 - 3)2
[Replace (x1, y1) with (11, 3) and (x2, y2) with (7, - 1).]

BC = (- 4)2+(- 4)2=16+16=32
[Simplify.]

CD = (3 - 7)2+(3 - (- 1))2
[Replace (x1, y1) with (7, - 1) and (x2, y2) with (3, 3).]

CD = (- 4)2+42=16+16=32

DA = (7 - 3)2+(7 - 3)2=16+16=32
[Replace (x1, y1) with (3, 3) and (x2, y2) with (7, 7).]

Perimeter of the quadrilateral ABCD = AB + BC + CD + DA

= 32+32+32+32
[Substitute the values.]

= 432 = 22.62

The perimeter of quadrilateral ABCD is 22.62 units.


Correct answer : (2)
 18.  
If AB is a line segment and P is the midpoint, then which of the following is true?
a.
BP = AB
b.
AP = AB
c.
AB = AP 2
d.
AP = BP


Solution:

AB is the line segment and P is the midpoint.

P divides the line segment AB into two equal parts AP and BP.

AP = BP = AB / 2 .


Correct answer : (4)
 19.  
Midpoint divides the line-segment into _____.
a.
Two unequal parts
b.
Four equal parts
c.
Two equal parts
d.
Three equal parts


Solution:

Midpoint divides the line-segment into two equal parts.


Correct answer : (3)
 20.  
Find the midpoint of the line-segment AB in the graph.


a.
(5 2 , 1 2)
b.
(2, 3)
c.
(4, 5)
d.
(1 2, 5 2)


Solution:

From the graph, the coordinates of A are (- 3, - 1) and B are (4, 6).

Midpoint = (x1+x22, y1+y22)
[Use the midpoint formula.]

Midpoint of AB = (- 3 + 42, - 1 + 62)
[Replace (x1, y1) with (- 3, - 1) and (x2, y2) with (4, 6).]

Midpoint = (1 / 2 , 5 / 2)
[Simplify.]

Midpoint of the line segment AB = (1 / 2 , 5 / 2)


Correct answer : (4)

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