Distance Formula Worksheet

**Page 1**

1.

Find the distance between the points (2, 3) and (5, 7).

a. | $\sqrt{7}$ units | ||

b. | 6 units | ||

c. | 25 units | ||

d. | 17 units | ||

e. | 5 units |

Let A(

AB =

[Distance between two points.]

=

[Simplify.]

=

So, the distance between the points is 5 units.

Correct answer : (5)

2.

Find the distance between two points A and B shown in the graph.

a. | 4 units | ||

b. | 34 units | ||

c. | $\sqrt{2}$ units | ||

d. | 5.83 units | ||

e. | 6 units |

Co - ordinates of A are (-1, 2) and B are (2, -3).

[Write the coordinates from the graph.]

Distance between the points AB =

[(

=

[Simplify.]

=

So, the distance between two points A and B is approximately 5.83 units.

Correct answer : (4)

3.

The point (2, $p$) lies in the first quadrant, at a distance of 3 units form (2, 2). Find the possible value of $p$.

a. | 5 | ||

b. | 1 | ||

c. | 2 | ||

d. | 3 |

Let (

3 =

[The distance between the points is 3 units.]

Þ 3 =

± 3 =

[Solve for

Since the point (2,

So, the possible value of

Correct answer : (1)

4.

Find the distance between the two points A and B shown in the graph.

a. | 10 units | ||

b. | 0 units | ||

c. | $\sqrt{28}$ units | ||

d. | 14 units | ||

e. | 48 units |

Co - ordiantes of A are (3, 4) and B are (- 3, - 4).

Distance between A and B =

[(

=

=

[Simplify.]

The distance between the points A and B is 10 units.

Correct answer : (1)

5.

Find the distance between the points (2.8, 3.3) and (-7.4, 1).

a. | 10 units | ||

b. | 10.45 units | ||

c. | 5.14 units | ||

d. | 11 units | ||

e. | 4.77 units |

Let (

Distance between the points,

[Use distance formula.]

=

=

[Simplify.]

The distance between the points is approximately 10.45 units.

Correct answer : (2)

6.

A line segment AB is of length 6 units, whose end points are A(0, 3) and B($a$, 3). Find the possible values of $a$.

a. | - 3 and 3 | ||

b. | $\sqrt{6}$ | ||

c. | - 6 and 6 | ||

d. | 6 only | ||

e. | - 36 and 36 |

Let A(

6 =

[The distance between the points is 6 units.]

[Solve for

So, the possible values of

Correct answer : (3)

7.

The distance from origin to a point A(3$q$, 5$q$) is 7$\sqrt{34}$ units. Find the possible values of $q$.

a. | $\sqrt{34}$ | ||

b. | 7 only | ||

c. | - 7 and 7 | ||

d. | - 49 and 49 |

The distance from origin to a point A(3

7

[(

7

49 × 34 = 34

[Square the both sides of the equation.]

49 =

[Cancel the common factors.]

± 7 =

So, the possible values of

Correct answer : (4)

8.

Choose the coordinates of the point P, which is 10 units from the point Q(3, 4).

a. | (- 3, 4) | ||

b. | (5, 5) | ||

c. | (4, 0) | ||

d. | (- 3, - 4) |

The distance between Q and P is 10 units.

Distance between (3, 4) and (5, 5) =

[(

=

[Simplify.]

Distance between (3, 4) and (- 3, - 4) =

[(

=

[Simplify.]

Distance between (3, 4) and (- 3, 4) =

[(

=

[Simplify.]

Distance between (3, 4) and (4, 0) =

[(

=

[Simplify.]

The point (- 3, - 4) is at a distance of 10 units from Q.

So, the coordinates of P are (- 3, - 4).

Correct answer : (4)

9.

The point B is the reflection of the point A(4, - 7) through the origin. Find the length of the line segment AB.

a. | 0 units | ||

b. | 16.12 units | ||

c. | 15 units | ||

d. | 17 units | ||

e. | 11 units |

So, the coordinates of B are (- 4, 7).

The distance between two points (

Let (

Distance between A and B =

[Use distance formula.]

=

=

[Simplify.]

The length of the line segment AB is approximately 16.12 units.

Correct answer : (2)

10.

The diagonals of the rectangle PQRS intersect each other at the point O, as shown in the figure. Find the length of the line segment OP.

a. | 3.6 units | ||

b. | $\sqrt{5}$ units | ||

c. | 13 units | ||

d. | 3 units | ||

e. | 4 units |

The distance between the two points (

Distance between the points O and P =

[Take (

=

[Simplify.]

=

[Simplify.]

So, the length of the line segment OP is approximately 3.6 units.

Correct answer : (1)