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Math A M$2 Worksheet

Lesson 9-2: Distance and Midpoint Formula Period:

Name:

Aim Students will be able to use the distance and midpoint formula. Do Now

Graph points A(-3, 4), B(1, 1), and C(-3, 1), then connect these points.

1. 2.

Find the length of AC and BC. ABC is a right triangle. Use the Pythagorean Theorem to write an equation relating to AC, BC and AB.

3.

Substitute values for AC and BC in the equation you wrote and solve the equation to find AB.

Lesson

1. The Distance Formula: The distance d between any two points (x1, y1) and (x2, y2) is d = (x2 ­ x1) + (y2 ­ y1) 2. a. X(4, 1) and Y(1, 4)

2 2

(x2, y2)

d

(y2 ­ y1)

Exercise: Find the distance of XY.

(x1, y1)

(x2 ­ x1)

b.

X(2, 9) and Y(-2, -9)

c.

X(5, -11) and Y(12, -7)

d.

X(0, -2) and Y(4, 1)

3.

The Midpoint Formula: The midpoint M of a line segment with endpoints A(x1, y1) and B(x2, y2) is

M

(x2, y2) (y1 + y2)/2

M:(

4.

x1 + x2 y1 + y2 , ) 2 2

(x1, y1)

Exercise: Find the midpoint of XY.

(x1 + x2)/2

!

a.

X(4, 1) and Y(1, 4)

b.

X(2, 9) and Y(-2, -9)

c.

X(5, -11) and Y(12, -7)

d.

X(3, 6) and Y(11, -8)

1

Mr. Lin

Math A M$2 Homework

1.

Lesson 9-2: Distance and Midpoint Formula

Period:

Name:

y A

Approximate AB, CD and EF to the nearest tenth of a unit. 1) AB = _______

E

C

2) CD = _______

B

x

3) EF = _______

F 2.

D

Find the distance and midpoint of XY. 1) X(0, 4) and Y(0, -4)

3.

Find the perimeter of the following figure.

y A B

x C

2) X(7, 1) and Y(-7, 1)

D

3) X(4, 3) and Y(-4, -3)

4) X(9, 2) and Y(3, -6)

2

Mr. Lin

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