Distance & Midpoint Formula

Distance

100

What is the distance formula?

d=√(x₂-x₁)²+(y₂-y₁)²

200

What is the distance between (8,11) and (8,4)?

7

300

Given the points A and B where A is at coordinates ( 2, -5 ) and B is at coordinates ( -3, -7 ) on the line segment AB, find the length of AB.

√29 or 5.39

400

Classify triangle ABC as scalene, isosceles, or equilateral A(3,1), B(4,2), C(1,3)

scalene

500

Classify triangle ABC as scalene, isosceles, or equilateral A(-4,3), B(4,3), C(0,4)

isosceles

Midpoint

100

What is the midpoint formula?

M(((x₁+x₂)/2),((y₁+y₂)/2)))

200

Given the points A and B where A is at coordinates ( 2,-5 ) and B is at coordinates ( -3,-7 ) on the line segment AB, find the midpoint of AB.

(-.5,-6)

300

Find the midpoint of the line segment AB where point A is at ( 0, 2 ) and point B is at ( -1, - 4 ).

(-.5,-1)

400

Find the midpoint of the line segment joining the points ( 1, - 4 ) and ( - 4, 2 )

(-1.5,-1)

500

Write an equation for the perpendicular bisector of the line segment joining A(-1, 4) and B(5, 2)

y=3x-3

Slopes

100

Are these Parallel, Perpendicular, or Neither: y = 5x + 4 and y = 5x - 4.

Neither

200

Are these Parallel, Perpendicular, or Neither: y = 5x + 4 and y = -1/5x + 14.

Perpendicular

300

What is the slope of a line perpendicular to y=5/4x +7?

-4/5

400

Write the equation of a line that is parallel to the line y = 3x + 1 and passes through the point (1, 2).

y=3x - 1

500

Write the equation of a line that is Perpendicular to y=1/4x-2 and crosses through the point (-3, -3).

y = -4x -15

Which Quadrilateral?

100

What do you have to prove in order for a quadrilateral to be a rhombus?

2 sets of parallel sides (same slopes)

all side lengths are equal

200

What do you have to prove for a quadrilateral to be considered as a square?

2 sets of parallel sides (same slopes)

4 right angles (perpendicular slopes)

all side lengths are the same length

300

Prove that the following points represent the vertices of a parallelogram: 

A: ( 2 , 4 ) , B: ( 4 , -3 ) , C: ( 9 , -6 ) , D: ( 7 , 1 ) 

slope of AB & CD =  −7/2  

slope of BC & AD = −3/5 

measure of AB & CD = √ 53
measure of BC & AD =  √ 34

400

Is the quadrilateral a rhombus with the vertices:
 A(0,3),  B(4,0),  C(8,3),  D(5,6) 

NO, the sides do not make 4 right angles or are all the same length

500

Is the quadrilateral with vertices A(1,1), B(4,3), C(7,1), D(4,−1)  a rectangle?

NOT A Rectangle

All side lengths are 5

AB is parallel to CD

BC is a parallel AD

angles do not form perpendicular slopes