Coordinate Geometry Worksheet

Coordinate Geometry Worksheet
  • Page 1
 1.  
What is located at (3, 3)?

a.
Palm tree
b.
Book store
c.
Food mart
d.
Pizza corner


Solution:

Start at zero.

As the first number in the ordered pair represents the number of spaces you have to move right, move 3 spaces to the right.

As the second number in the ordered pair represents the number of spaces you have to move up, move 3 spaces up.

So, the Food mart is located at the point (3, 3).


Correct answer : (3)
 2.  
ABCD is a square. The coordinates of C are (- 4, - 4). What are the coordiantes of A?


a.
(- 8, - 8)
b.
(- 4, 4)
c.
(4, 4)
d.
(4, - 4)


Solution:

O is the origin.
[From the figure.]

ABCD is symmetrical with respect to x-axis and y-axis.
[ABCD is a square.]

D is the reflection of C w.r.t x-axis.
B is the reflection of C w.r.t y-axis.
A is the reflection of B w.r.t x-axis.

The coordinates are D(- 4, 4) , B(4, - 4) and A(4, 4).

The coordinates of A are A(4, 4).


Correct answer : (3)
 3.  
PQRS is a rectangle. The coordinates of M are M(8, 0) and N are N(0, 4). What are the coordinates of P and Q?

a.
(8, 4 ) and (8, - 4 )
b.
( 8, - 4 ) and (- 8, 4 )
c.
(-8, - 4 ) and (8, - 4)
d.
(- 8, - 4 ) and (- 8, 4 )


Solution:

PQRS is symmetrical w.r.t the coordinate axis.
[From the figure.]

Coordinates of R are R(8, 4).
[OM = 8, ON = 4.]

Coordinates of Q, P and S are Q(8, - 4), P(- 8, - 4) and S(- 8, 4).
[From Step 1.]

The Coordinates of P and Q are P(- 8, - 4) and Q(8, - 4).


Correct answer : (3)
 4.  
OPQR is a Rhombus. Find the coordinates of Q and R, if the coordinates of P are P(3, 6).

a.
(- 6, 0) and ( 3 , - 6 )
b.
(6, 0) and (- 3 , 6)
c.
( 0 , 6) and ( - 3 , - 6 )
d.
(6, 0) and (3 , - 6)


Solution:

Lines of symmetry for the given Rhombus are PR and OQ.

Coordinates of R are R(3, - 6)
[R is the reflection of P on x - axis.]

The coordinates of M are M(3, 0)
[M lies on x - axis.]

The coordinates of Q and R are Q(6, 0) and R(3, - 6)
[OM = QM.]


Correct answer : (4)
 5.  
ABCD is a parallelogram. The coordinates of B and C are B(3, - 3) and C(4 , 3). Find the coordinates of A.


a.
( 4, 3)
b.
(- 4, - 3)
c.
(- 4, 3)
d.
( 4, - 3)


Solution:

Coordinates of C are (4, 3).
[Given data.]

O is the midpoint of AC.
[Diagonals of the parallelogram bisect each other.]

Coordinates of A are A(- 4, - 3).
[Coordinates of O are O(0,0). Apply midpoint formula.]


Correct answer : (2)
 6.  
OQ = 10. mORQ = 90, PM = 3 RM. Write the coordinates of P.


a.
P(15, 5)
b.
P(5, 15)
c.
P(15, 15)
d.
P(5, 5)


Solution:

Coordinates of Q are Q(10, 0)
[OQ = 10.]

Coordinates of M are M(5 , 0)
[Longer diagonal of the kite is the perpendicular bisector.]

RM = QM.
[mORQ = 90°
mMRQ = 45°
ΔRMQ is isosceles right angle triangle.]

RM = 5 .

Coordinates of R are (5 , 5 )
[Step 2 & 4.]

PM = 3 RM
= 15.

Coordinates of P are P(5, 15 )
[Step 6 & step 2.]


Correct answer : (2)
 7.  
PQRS ia a parallelogram. Coordinates of Q and R are Q(8, 2) and R(4, - 2). What would be the coordinates of P, Q, R and S if the parallelogram is shifted so that SR is placed on the x-axis with S as the origin?

a.
(- 4, 4), (- 16, - 4), (- 12, 0) and (0, 0)
b.
( 4, - 4), (8 , 2 ) , (4, - 2 ) and (0, 0)
c.
(4, 4), (16, 4), (12, 0) and (0, 0)
d.
(- 4, 2 ), (16, 4) , (12, 0) and (- 8, - 2)


Solution:

The original position of P and S are P(- 4, 2) and S(- 8, - 2)
[Diagonals of the parallelogram bisect each other.]

When S coincides with the origin and SR is placed on x-axis, The coordinates of S and R are S(0,0) and R(12, 0)
[SR = 8 + 4 = 12.]

The new coordinates of P and Q are P(4, 4) and Q(16, 4)
[x-coordinates change to x+8, y-coordinates change to y+2.]

The new coordinates of P, Q , R and S are (4, 4) , (16, 4) , (12, 0) and (0, 0).


Correct answer : (3)
 8.  
The vertices of quadrilateral OABC are O(0, 0), A(28, 0), B(24, 8) and C(8, 24). Find the midpoint of the line joining the midpoints of OA and BC.


a.
(15, 8)
b.
(14, 0)
c.
(16, 16)
d.
(20, 24)


Solution:


Let P, Q, R and S be midpoints of OA, AB, BC and OC.

The coordinates of P, Q, R and S are P(28 / 2, 0), Q(28+24 / 2, 8 / 2), R(24+8 / 2, 8+24 / 2) and S(8 / 2, 24 / 2).
[Midpoint of the line joining points (x1 , y1) and (x2 , y2) is (x2+x12, y2+y12).]

The coordinates of P and R are (14, 0) and (16, 16).

Midpoint of the line joining the midpoint of OA and BC is (15, 8).
[ P and R are the midpoints of OA and BC.]


Correct answer : (1)
 9.  
PQRS is a parallelogram. OP : OS = 1 : 2. Coordinates of P and Q are P(3, 0) and Q(9, 0). Find the coordinates of R.


a.
(7, 6)
b.
(9, 6)
c.
(7, 7)
d.
(6, 6)


Solution:

OS = 21 × 3
[OP : OS = 1 : 2.]

Coordinates of S are S(0, 21× 3) = (0, 6 )
[S lies on y-axis.]

PQ = 9 - 3 = 6.
RS = 9 - 3 = 6.

x-coordiante of R = 6
[x-coordinate of S + PQ.]

y-coordinate of R = 6
[Same as y-coordinate of S.]

The coordinates of R are R(6, 6 )


Correct answer : (4)
 10.  
ABCD is an isosceles trapezoid. The coordinates of A and D are A (- 22, 0) and D (- 16, 10). Find the length of the line segment joining the midpoints of AD and BC.

a.
19
b.
5
c.
38
d.
10


Solution:

y-axis is the line of symmetry of the trapezoid.

Coordinates of B and C are B(22, 0) and C(16, 10).
[B is the reflection of A w.r.t x-axis and C is reflection of D w.r.t y-axis.]

Midpoint of AD is (- 22-162 , 102 ) = (- 19, 5)
[Midpoint of line joining (x1, y1 ) and (x2 , y2) is (x2+x12, y2+y12).]

Midpoint of BC is (22+162 , 102 ) = (19, 5)
[Same as step 3.]

Length of the line segment joining the midpoint of AD and BC = (19 - (-19))2 = (38)2 = 38


Correct answer : (3)

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