Sep 25­12:09 PM

Slope, Distance and Midpoint

• The slope formula is used when we need to show that two lines or line segments are either parallel (equal slopes) or perpendicular (slopes are negative reciprocals).

• The distance formula is used when we need to calculate the length of a line segment, or in other words when we wish to find the distance between two points.

The midpoint formula is used when we need to find the center or middle of a line segment.

Sep 25­12:23 PM

Example #1: Show that quadrilateral ABCD is a parallelogram. The given vertices are A(4,-6), B(0,-8), C(-1,0) and D(3,2)

Sep 25­12:33 PM

You try:Show that quadrilateral given by the vertices C(6,4), A(4,-1), T(-3,-2) and S(-1,3) is a parallelogram.

Sep 25­12:27 PM

Example #2: Show that triangle ABC is isosceles. The given vertices are A(-2,5), B(6,-1) and C(5,6).

Sep 25­12:38 PM

You try:Show that Triangle JKL given by the vertices J(-1,-2), K(-7,-2) and L(-4,6) is isosceles.

Sep 25­12:29 PM

Example #3: Show that the diagonals of quadrilateral ABCD have the same midpoint. The given vertices are A(5,1), B(7,-1), C(1,-3) and D(-1, -1).

Sep 25­12:39 PM

You try:Given quadrilateral QRST with vertices Q(2,0), R(4,-6), S(9,1) and T(7,7), show the diagonals QS and RT bisect each other.

Feb 15­7:34 AM

  C

A

B

How could we determine which type of triangle this is?

Scalene?Right Angled?Isosceles?Equilateral?

Feb 15­7:44 AM

Slope

Distance

Midpoint

Feb 15­8:08 AM

Find the Slope, Midpoint and Distance for the lines joining the points with the given coordinates (include sketches of each line)a. (4,2) , (9, ­3)

b. (8,­6) , (­7,­6)

c. (­3,8) , (­3,­2)

Feb 15­8:11 AM

a. (4,2) , (9, ­3)  b. (8,­6) , (­7,­6)  c. (­3,8) , (­3,­2)

Feb 15­7:48 AM

Practice Problems ­ show your formula and express your answer as fraction reduced to simplest form. Do not write answers as mixed fractions.                                                                1. Find the slope of AB.                                                                 

2. Find the slope of CD.

3. Find the slope of EF.

mAB =35

mEF =­23

mCD = 32

Feb 15­7:58 AM

How can we determine if lines are parallel or perpendicular?

Two lines have the same slope if and only if they are parallel.

m1 = m2 iff  ℓ1 || ℓ2    

Two lines are perpendicular if and only if the product of their slopes is ­1 (or slopes are negative reciprocals of each other). 

             ℓ1┴ ℓ2  iff  m1  m2 = ­1x

Feb 15­7:50 AM

Use slope to determine if ΔABC is a right angled triangle.

  C

A

B

Sep 25­2:29 PM

Complete Questions on Handout