Lesson

Distance and Midpoints

1-3

Ohio Content Standards:

Ohio Content Standards:

• Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

Ohio Content Standards:

• Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.

Distance Formula

Distance Formula

• Number Line

P Q

a b

Distance Formula

• Number Line

P Q

a b

Distance Formula

• Number Line

» PQ = l b – a l or l a – b l

Distance Formula

Distance Formula

• Coordinate Plane

Distance Formula

• Coordinate Plane– The distance d between

two points with coordinates (x1, y1) and (x2, y2) is given by

• Coordinate Plane– The distance d between

two points with coordinates (x1, y1) and (x2, y2) is given by

Distance Formula

221212 yyxx

Use the number line to find QR.

Use the number line to find QR.

RQ

-8 -7 -6 -5 -4 -3 0-2 -1

Find the distance between E(-4, 1) and F(3, -1).

Midpoint

Midpoint

• Number Line

P Q

a b

Midpoint

• Number Line

P Q

a b

Midpoint

• Number Line

»

2

ba

Midpoint

Midpoint

• Coordinate Plane

Midpoint

• Coordinate Plane– The coordinates of the

midpoint of a segment whose endpoints have coordinates (x1, y1) and (x2, y2) are

Midpoint

• Coordinate Plane– The coordinates of the

midpoint of a segment whose endpoints have coordinates (x1, y1) and (x2, y2) are

2,

22121 yyxx

The coordinates on a number line of J and K are -12 and 16, respectively. Find the

coordinate of the midpoint of JK.

Find the coordinates of the midpoint of GH for G(8, -6)

and H(-14, 12).

Find the coordinate of D if E(-6, 4) is the midpoint of DF

and F has coordinates (-5, -3).

What is the measure of PR if Q is the midpoint of PR?

P QR

6 - 3x

14x + 2

Assignment:

Pgs. 25 - 2714 - 44 evens58 - 68 evens