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

Coordinate Geometry Worksheet - Page 6

Coordinate Geometry Worksheet
  • Page 6
 51.  
Find the location of the vertex D, if ABCD forms a square.

a.
(6, 6)
b.
(6, 3)
c.
(3, 3)
d.
(3, 6)


Solution:

From the graph, the vertex A is (3, 3), the vertex B is (6, 3), and the vertex C is (6, 6).


If ABCD forms a square, then the x-coordinate of the vertex D should be equal to the x-coordinate of the vertex A and the y-coordinate of the vertex D should be equal to the y-coordinate of the vertex C and it looks like below.

From the above graph, the vertex D is (3, 6).

So, the location of the other vertex D is (3, 6).


Correct answer : (4)
 52.  
Find the location of the vertex R, if PQRS forms a rectangle.

a.
(6, 8)
b.
(6, 2)
c.
(2, 6)
d.
(8, 6)


Solution:

From the graph, the vertex P is (2, 2), the vertex Q is (2, 8), and the vertex S is (6, 2).


If PQRS forms a rectangle, then the x-coordinate of the vertex R should be equal to the x-coordinate of the vertex S and the y-coordinate of the vertex R should be equal to the y-coordinate of the vertex Q.

From the above graph, the vertex R is (6, 8).

So, the location of the vertex R is (6, 8).


Correct answer : (1)
 53.  
Which is the location of the vertex N, if KLMN is a square?

a.
(- 9, 9)
b.
(9, - 9)
c.
(8, 9)
d.
(9, 9)


Solution:

From the graph, the vertex K is (6, 9), the vertex L is (6, 6), and the vertex M is (9, 6).


If KLMN forms a square, then the x-coordinate of the vertex N should be equal to the x-coordinate of the vertex M and the y-coordinate of the vertex N should be equal to the y-coordinate of the vertex K and it looks like below.

From the above graph, the vertex N is (9, 9).

So, the location of the vertex N is (9, 9).


Correct answer : (4)
 54.  
Identify the relationship between the coordinates of the vertices P and Q.

a.
P and Q have same y-coordinate
b.
y-coordinate of P is 2 units less than y-coordinate of Q.
c.
x-coordinate of P is 2 units more than x-coordinate of Q.
d.
P and Q have same x-coordinate


Solution:

From the graph, the ordered pairs of P and Q are (3, 3) and (5, 3).

As the second number in the ordered pairs of P and Q are same, there is no change in their y-coordinates.

The relationship between the coordinates of the vertices P and Q is, both have same y-coordinate.


Correct answer : (1)
 55.  
Identify the relationship between the coordinates of the vertices C and D.


a.
Both have same x-coordinate
b.
x-coordinate of C is 4 more than x-coordinate of D
c.
y-coordinate of C is 4 less than y-coordinate of D
d.
Both have same y-coordinate


Solution:

From the graph, the ordered pairs of C and D are (7, 6) and (7, 2).

As the first number in the ordered pairs of C and D are same, there is no change in their x-coordinates.

The relationship between the coordinates of the vertices C and D is, both have same x-coordinate.


Correct answer : (1)
 56.  
How far is the Cafeteria from the Lake?

a.
4 units
b.
5 units
c.
3 units
d.
6 units


Solution:

The line joining the Lake and the Cafeteria is a vertical line segment.

The length of a vertical line segment on a coordinate plane equals the difference between the y-coordinates.

The Cafeteria is located on the ordered pair (4, 2) and the Lake is on the ordered pair (4, 7).

So, the distance between the Cafeteria from the Lake = 7 - 2 = 5.
[Difference between the y-coordinates.]

The Cafeteria is 5 units far from the Lake.


Correct answer : (2)
 57.  
Find the distance between the Playground and the Tenniscourt.


a.
5 units
b.
3 units
c.
4 units
d.
2 units


Answer: (b)


Correct answer : (2)
 58.  
Find the length of the line segments joining the points A(7, 4) and B(9, 4).
a.
20 units
b.
16 units
c.
9 units
d.
2 units


Answer: (d)


Correct answer : (4)
 59.  
Find the length of the line segments joining the points A(9, 2) and B(13, 2).
a.
4 units
b.
24 units
c.
22 units
d.
13 units


Answer: (a)


Correct answer : (1)
 60.  
Find the length of the line segments joining the points M(- 2, 3) and N(- 2, 5).
a.
2 units
b.
5 units
c.
7 units
d.
3 units


Answer: (a)


Correct answer : (1)

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