Coordinate Geometry Worksheet

**Page 2**

11.

ABCD is a rectangle . The vertices of A are (- 8, - 3). Find the slope of the diagonal $\stackrel{\u203e}{\mathrm{AC}}$.

a. | $\frac{8}{3}$ | ||

b. | $\frac{3}{4}$ | ||

c. | $\frac{8}{9}$ | ||

d. | $\frac{3}{8}$ |

The coordinates of B, C and D are B(8, - 3), C(8, 3) and D(- 8, 3).

Slope of AC is =

[Slope of line passing through (

Correct answer : (4)

12.

OABC is a quadrilateral. The coordinates of A, B and C are A(28, 0) , B(40, 20) and C(20, 44) . Find the slope of the line joining the midpoints of $\stackrel{\u203e}{\mathrm{AB}}$ and $\stackrel{\u203e}{\mathrm{BC}}$.

a. | - $\frac{23}{6}$ | ||

b. | - 6 | ||

c. | - $\frac{11}{2}$ | ||

d. | - $\frac{11}{3}$ |

Midpoint of OA = (

[Step 1.]

Midpoint of AB = (

[Step 1.]

Midpoint of BC = (

[Step 1.]

Midpoint of OC = (

= -

Slope of the line segment joining the midpoint of AB & BC =

[Slope of the line segment joining the points (

Correct answer : (3)

13.

ABCD is a square. The coordinates of A & B are A(5, 0) and B(13, 0). ACPQ is another square with point D inside it. Find the coordinates of P and Q.

a. | (13, 8) and (5, 0) | ||

b. | (5, 16) and (- 3, 8) | ||

c. | (18, 0) and (8, 0) | ||

d. | (21, 0) and (13, - 16) |

CD = QD.

Square with AC as side will have D as its point of intersection of the diagonals.

The coordinates of C and D are (13, 8) and (5, 8).

[Since ABCD is a square, AB = AD

= 5

= 8 + 8

= 16

= 5 - 8

= - 3

The coordinates of P and Q are (5, 16) and (- 3, 8).

Correct answer : (2)

14.

Coordinates of the vertices of a quadrilateral are A(3, 4), B(4, 6), C(3, 8) and D(2, 6). Identify the figure without drawing it.

a. | Rectangle | ||

b. | Square | ||

c. | Rhombus | ||

d. | Parallelogram |

[Length of a line segment =

Slope of AB =

Slope of AD =

Slope of AM × slope of AD = 2 × - 2 = - 4.

AB and AD are not perpendicular.

ABCD is a rhombus.

[ABCD is not a square as the adjacent sides are not perpendicular.]

Correct answer : (3)

15.

The vertices of a quadrilateral are A(2, 5), B(6, 1), C(8, 3) and D(4, 7). Identify the quadrilateral with out making the diagram.

a. | None of these | ||

b. | Rectangle | ||

c. | Rhombus | ||

d. | Square |

[Length of line segment passing through (

BC =

CD =

DA =

AB = CD ; BC = AD.

[ABCD is a parallelogram.]

Slope of AB =

[Slope of line passing through (

Slope of BC =

Slope of AB × slope of BC = - 1 × 1 = - 1

AB

[Product of slope = - 1.]

Since ABCD is a parallelogram and

Correct answer : (2)

16.

ABCD is an isosceles trapezoid. What will be the coordinates of D if the trapezoid is moved towards right so that A is placed at the origin and $\stackrel{\u203e}{\mathrm{AB}}$ is on the x - axis? [Given A(- 8, 0), B(8, 0) and C(5, 6). ]

a. | (- 3, 6) | ||

b. | (3, 6) | ||

c. | (- 3, - 6) | ||

d. | (3, - 6) |

BP = 8 - 5 = 3

AQ = 8 - 5 = 3

Coordinates of D are (- 5, 6).

When trapezoid moves towards right, A coincides with O.

New coordinates of D are ( (- 5 + 8), 6) = (3, 6)

Correct answer : (2)

17.

OABC is a parallelogram. Coordinates of A and C are (12, 0) and (5, 5). Find the product of the slope of the side $\stackrel{\u203e}{\mathrm{AB}}$ and diagonal $\stackrel{\u203e}{\mathrm{OB}}$.

a. | $\frac{5}{6}$ | ||

b. | $\frac{5}{17}$ | ||

c. | $\frac{5}{17}$ | ||

d. | $\frac{17}{5}$ |

Coordinates of C are (5, 5).

OA = 12

BC = 12

Coordinates of B are ((5+12), 5) = (17, 5)

[OA = BC, OA parallel BC.]

Slope of AB =

[Slope of line passing through (

Slope of OB =

Product of the slopes =

Correct answer : (3)

18.

In the quadrilateral OABC, slope of the diagonal $\stackrel{\u203e}{\mathrm{OB}}$ is $\frac{2}{3}$, slope of $\stackrel{\u203e}{\mathrm{AB}}$ is $\frac{3}{4}$. If the coordinates of A are (6, 0), then find the length of $\stackrel{\u203e}{\mathrm{AB}}$ rounded to the nearest whole number.

a. | 55 | ||

b. | 60 | ||

c. | 50 | ||

d. | 65 |

Let the coordinates of B are (

[Slope of a line passing through (

Slope of AB =

Slope of AB =

[Slope of line passing through (

[From step 3 and step 4.]

[Substitute the value of

[From step 5 and step 6.]

3 × 3(

9

[Substitute

The coordinates of B are (54, 36)

AB =

[Rounded to the nearest whole number.]

Correct answer : (2)

19.

ABCD is a rectangle. The coordinates of the vertices are given as A(4, 7) , B(19, 7) . The length of $\stackrel{\u203e}{\mathrm{AB}}$ is 15 units and $\stackrel{\u203e}{\mathrm{AC}}$ is 17 units. Find the slope of $\stackrel{\u203e}{\mathrm{BD}}$.

a. | - $\frac{15}{8}$ | ||

b. | $\frac{15}{8}$ | ||

c. | $\frac{8}{15}$ | ||

d. | - $\frac{8}{15}$ |

AC = 17

BC = 8

[BC

Coordinates of C are (19, 7 + 8) = (19, 15)

[

Coordinates of D are (4, 7 + 8) = (4, 15)

[

Coordinates of B are B(19, 7)

[Given.]

Slope of BD =

Correct answer : (4)

20.

Find whether the diagonals of the isosceles trapezoid intersect at right angle. [Given $a$ = 11, $b$ = 4 and $c$ = 6. ]

a. | No | ||

b. | Yes |

[From the question.]

Coordinates of C are (4, 6)

[OA parallel to CB.]

[

Slope of OB =

Slope of AC =

Product of the slopes =

So, the diagonals of the isosceles trapezoid do not intersect at right angle.

Correct answer : (1)