Coordinate Geometry Worksheet

**Page 1**

1.

What is located at (3, 3)?

a. | Palm tree | ||

b. | Book store | ||

c. | Food mart | ||

d. | Pizza corner |

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) |

[From the figure.]

ABCD is symmetrical with respect to

[ABCD is a square.]

D is the reflection of C w.r.t

B is the reflection of C w.r.t

A is the reflection of B w.r.t

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 ) |

[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) |

Coordinates of R are R(3, - 6)

[R is the reflection of P on

The coordinates of M are M(3, 0)

[M lies on

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) |

[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. $m$$\angle $ORQ = 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) |

[OQ = 10.]

Coordinates of M are M(5 , 0)

[Longer diagonal of the kite is the perpendicular bisector.]

RM = QM.

[m

m

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) |

[Diagonals of the parallelogram bisect each other.]

When S coincides with the origin and SR is placed on

[SR = 8 + 4 = 12.]

The new coordinates of P and Q are P(4, 4) and Q(16, 4)

[

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 $\stackrel{\u203e}{\mathrm{OA}}$ and $\stackrel{\u203e}{\mathrm{BC}}$.

a. | (15, 8) | ||

b. | (14, 0) | ||

c. | (16, 16) | ||

d. | (20, 24) |

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

The coordinates of P, Q, R and S are P(

[Midpoint of the line joining points (

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) |

[OP : OS = 1 : 2.]

Coordinates of S are S(0,

[S lies on

PQ = 9 - 3 = 6.

RS = 9 - 3 = 6.

[

[Same as

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 $\stackrel{\u203e}{\mathrm{AD}}$ and $\stackrel{\u203e}{\mathrm{BC}}$.

a. | 19 | ||

b. | 5 | ||

c. | 38 | ||

d. | 10 |

Coordinates of B and C are B(22, 0) and C(16, 10).

[B is the reflection of A w.r.t

Midpoint of AD is (

[Midpoint of line joining (

Midpoint of BC is (

[Same as step 3.]

Length of the line segment joining the midpoint of AD and BC =

Correct answer : (3)