To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Cartesian Coordinates Worksheet

Cartesian Coordinates Worksheet
  • Page 1
 1.  
If (0, 0) (2, 4) (8, 0) (x, y) are the vertices of a parallelogram, then find the length of the longest diagonal if (x and y) are positive integers.

a.
6 units
b.
10.77 units
c.
14.42 units
d.
15.62 units


Solution:

The sides AB and CD are parallel, so the y-coordinate of (2, 4) and (x, y) is same.
[The sides of the parallelogram are parallel.]

y = 4
[y-coordinate of B is 4.]

x = 8 + 2 = 10
[x-coordinate of B is 2.]


From the figure and the given coordinates, the vertex (x, y) is (10, 4).

The longest diagonal is AC. The distance between A and C is (x2-x1)²+(y2-y1)²
[Use distance formula.]

= (10-0)²+(4-0)²
[Substitute the values.]

= 100 + 16
[Evaluate the exponents.]

= 116 units
[Simplify.]

The length of the longest diagonal is 116 units.


Correct answer : (2)
 2.  
Find the distance between the points (9, - 3) & (- 4, 2).
a.
21.928 units
b.
13.928 units
c.
16.928 units
d.
18.928 units


Solution:

The distance between the points P(x1, y1) and Q(x2, y2) in the coordinate plane is d = (x1-x2)2+(y1-y2)2.
[Formula.]

d = (9 - (-4))2+((-3) - 2)2
[Substitute.]

= 169 + 25
[Evaluate the powers.]

= 194
[Simplify.]

= 13.928 units
[Find the square root.]


Correct answer : (2)
 3.  
Find the midpoint of the line segment joining the points (8, 4) and (- 2, - 2).
a.
(- 3, 1)
b.
(3, 1)
c.
(3, - 1)
d.
(- 3, - 1)


Solution:


The midpoint of the line segment with endpoints (8, 4) and (- 2, - 2) is (8 - 22, 4 - 22).
[Use the formula.]

= (62, 22)

= (3, 1)


Correct answer : (2)
 4.  
Find the distance between the points (2, 4) & (- 7, 2).
a.
9.219 units
b.
21.219 units
c.
17.219 units
d.
19.219 units


Solution:

The distance between the points P(x1, y1) and Q(x2, y2) in the coordinate plane is d = (x1-x2)2+(y1-y2)2.
[Formula.]

d = (2 - (-7))2+(4 - 2)2
[Substitute.]

= 81 + 4
[Evaluate the powers.]

= 85
[Simplify.]

= 9.219 units
[Find the square root.]


Correct answer : (1)
 5.  
Find the midpoint of the line segment joining the points (6, 4) and (4, 6).
a.
(5, - 5)
b.
(- 5, 5)
c.
(5, 5)
d.
(- 5, - 5)


Solution:

The midpoint of the line segment with end points (a, b) and (c, d) is (a + c2, b + d2).
[Formula.]

Midpoint of the line segment with end points (6, 4) and (4, 6) = (6 + 42, 4 + 62)

= (102, 102)

= (5, 5)


Correct answer : (3)
 6.  
Find the perimeter of the triangle determined by the points (- 5, - 3), (0, - 1), (4, 4).
a.
14.14 units
b.
23.19 units
c.
14 units
d.
12 units


Solution:


Given points are A = (- 5, -3), B = (0, - 1), C = (4, 4) as shown.

Distance between points A and B is AB = (- 5 - 0)2+(-3 + 1)2 = 25 + 4 = 29 = 5.385
[Use formula.]

Distance between points B and C is BC = (0 - 4)2+(- 1 - 4)2 = 16 + 25 = 41 = 6.403
[Use formula.]

Distance between points C and A is CA = (4+5)2+(4+3)2 = 81 + 49 = 130 = 11.402
[Use formula.]

Perimeter of the figure formed by the points = AB + BC + CA

= 5.385 + 6.403 + 11.402

= 23.19


Correct answer : (2)
 7.  
Find the center and radius of the circle.
(x - 2)2 + (y - 2)2 = 4
a.
(2, - 2); 2
b.
(2, 2); 2
c.
(2, 2); 4
d.
(- 2, 2); 2


Solution:

(x - 2)2 + (y - 2)2 = 4

Center (h, k) = (2, 2)
[Compare with standard form of the circle (x - h)2 + (y - k)2 = r2.]

Radius, r = 4 = 2


Correct answer : (2)
 8.  
Which of the following points is in the third quadrant?
a.
(- 1, 2)
b.
(2, - 4)
c.
(- 4, - 2)
d.
(9, 9)


Solution:

Any point in the third quadrant should have negative x-coordinate and negative y-coordinate.

Hence, from the given choices, (- 4, - 2) is in the third quadrant.


Correct answer : (3)
 9.  
Evaluate |- 9|.
a.
- 9
b.
± 9
c.
9
d.
None of the above


Solution:

Because -9 < 0, |-9| = - (- 9) = 9
[Use Definition.]


Correct answer : (3)
 10.  
Evaluate |π - 12|.
a.
8.86
b.
± 8.86
c.
12
d.
- 8.86


Solution:

Because π 3.14, π - 12 is negative, so π - 12 < 0.

Thus, |π - 12| = - (π - 12) = 12 - π = 8.86


Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.