Distance and Midpoint Formula Worksheet

**Page 2**

11.

Find the distance between A(4, - 5) and B(5, - 8).

a. | 4.16 units | ||

b. | 3.16 units | ||

c. | 6.16 units | ||

d. | 5.16 units |

[Use the distance formula.]

[Replace (

[Subtract.]

[Simplify.]

[Find the positive square root.]

The distance between, A and B is 3.16 units.

Correct answer : (2)

12.

The distance between two points ($x$_{1}, $y$_{1}) and ($x$_{2}, $y$_{2}) is _____.

a. | $\sqrt{({x}_{2}-{x}_{1})+({y}_{2}-{y}_{1})}$ | ||

b. | $\sqrt{{({x}_{2}-{x}_{1})}^{2}+{({y}_{2}-{y}_{1})}^{2}}$ | ||

c. | $\frac{{x}_{1}+{y}_{1}+{x}_{2}+{y}_{2}}{2}$ | ||

d. | | (${x}_{2}+{y}_{2})-({x}_{1}+{y}_{1})|$ |

Correct answer : (2)

13.

Find the distance between A(- 5, 5) and B(- 7, 3) and round the solution to the nearest tenth.

a. | 5.8 units | ||

b. | 3.8 units | ||

c. | 2.8 units | ||

d. | 4.8 units |

[Use the distance formula.]

[Replace (

[Subtract.]

The distance between A and B is 2.8 units.

[Round the distance to the nearest tenth.]

Correct answer : (3)

14.

What is the distance between ($x$_{1}, $y$_{1}) and origin?

a. | $\sqrt{{{x}_{1}}^{2}+{{y}_{1}}^{2}}$ | ||

b. | $\sqrt{{{x}_{1}}^{2}-{{y}_{1}}^{2}}$ | ||

c. | $\sqrt{{x}_{1}+{y}_{1}}$ | ||

d. | $\sqrt{{x}_{1}-{y}_{1}}$ |

Distance

[Use the distance formula.]

[Replace (

[Subtract.]

Distance between (

Correct answer : (1)

15.

Which of the following ordered pairs is at a distance of 2 units from (5, 3)?

a. | (7, 4) | ||

b. | (10, 6) | ||

c. | (8, 7) | ||

d. | (7, 3) |

[Use the distance formula.]

Consider choice A, the distance between (5, 3) and (7, 4).

[Replace (

Consider choice B, the distance between (5, 3) and (10, 6).

[Replace (

Consider choice C, the distance between (5, 3) and (8, 7).

[Replace (

Consider choice D, the distance between (5, 3) and (7, 3).

[Replace (

Therefore, the point (7, 3) is at a distance of 2 units from (5, 3).

Correct answer : (4)

16.

Find the perimeter of the triangle ABC shown in the graph.

a. | 26.08 units | ||

b. | 30 units | ||

c. | 24 units | ||

d. | 20.92 units |

Distance

[Use the distance formula.]

AB =

[Replace (

AB =

=

[Simplify.]

BC =

[Replace (

BC =

=

[Simplify.]

CA =

[Replace (

CA =

=

[Simplify.]

Perimeter of ΔABC = AB + BC + CA

=

[Substitute the values.]

= 7.21 + 6.71 + 7 = 20.92

The perimeter of ΔABC = 20.92 units.

Correct answer : (4)

17.

Find the perimeter of quadrilateral ABCD shown in the graph.

a. | 13.24 units | ||

b. | 22.62 units | ||

c. | 24.78 units | ||

d. | 19.98 units |

Distance

[Use the distance formula.]

AB =

[Replace (

AB =

[Simplify.]

BC =

[Replace (

BC =

[Simplify.]

CD =

[Replace (

CD =

DA =

[Replace (

Perimeter of the quadrilateral ABCD = AB + BC + CD + DA

=

[Substitute the values.]

= 4

The perimeter of quadrilateral ABCD is 22.62 units.

Correct answer : (2)

18.

If AB is a line segment and P is the midpoint, then which of the following is true?

a. | BP = AB | ||

b. | AP = AB | ||

c. | AB = $\frac{\mathrm{AP}}{2}$ | ||

d. | AP = BP |

P divides the line segment AB into two equal parts AP and BP.

AP = BP =

Correct answer : (4)

19.

Midpoint divides the line-segment into _____.

a. | Two unequal parts | ||

b. | Four equal parts | ||

c. | Two equal parts | ||

d. | Three equal parts |

Correct answer : (3)

20.

Find the midpoint of the line-segment AB in the graph.

a. | ($\frac{5}{2}$ , $\frac{1}{2}$) | ||

b. | (2, 3) | ||

c. | (4, 5) | ||

d. | ($\frac{1}{2}$, $\frac{5}{2}$) |

Midpoint = (

[Use the midpoint formula.]

Midpoint of AB = (

[Replace (

Midpoint = (

[Simplify.]

Midpoint of the line segment AB = (

Correct answer : (4)