Parallel and Perpendicular Lines & Coordinate Geometry Proofs

Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is 3/2 given A(-2,4) and B(0,-8)

(-4/5,-16/5)

A parallelogram must be a rectangle when its (1) diagonals are congruent (2) diagonals are perpendicular (3) opposite sides are parallel (4) opposite sides are congruent

(1) diagonals are congruent

Which pair of lines is parallel? (1) y=4x-9 and y-4x=3 (2) y=2x and 2y=x-9 (3) 3y=-x+7 and y+2=3(x-5) (4) y+x=0 and y=x

(1) y=4x-9 and y-4x=3

Find the midpoint between the points (a,b) and (3a,c). (1) (a,b+c) (2) (-a,b-c/2) (3) (2a,b+c/2) (4) (4a,3a+c)

(3) (2a,b+c/2)

What is the length of the line segment that connects the points whose coordinates are (-3,5) and (-4,2)? (1) radical 11 (2) 11 (3) 5 (4) radical 10

(4) radical 10

Given the points L(2,-1) and U(6,5) find the midpoint of LU.

(4,2)

Given the points H(2x,-1y) and I(6x,5y) find the midpoint of HI.

(4x,2y)

Given the points A(3,2) and B(11,10), find the coordinates of point C such that AC:CB=1:3.

(5,4)

Given the lines 3x-y=9 and 3x-3y=8, determine if the lines are parallel, perpendicular or neither. Explain.

neither because the slopes are neither the same or opposite reciprocals

Write an equation of the line that is parallel to the y-axis and passes through the point (-7,4)

x=-7

Write an equation of the line that passes through the point (-1,0) and is perpendicular to the line 3x-2y=8.

y-0=-2/3(x+1)

Given points K(-5,2) and point J(5,0), write an equation of the line that goes through point K and is perpendicular to KJ.

y-2=5(x+5)

Write an equation of the line that passes through (2,5) and has a slope of 2.

y-5=2(x-2)

Write an equation of the line that is parallel to the x-axis and passes through the point (-4,6)

y-6=0(x+4)

Write an equation of the line that passes through the point (-3,6) and is perpendicular to the line y=-1/2x-4.

y-6=2(x+3)

Given the points L(2,-1) and U(6,5) find the length of LU in simplest radical form.

2 radical 13

What is the slope of the line that is perpendicular to 3x+2y=8?

2/3

Prove quadrilateral NEMO is a parallelogram given vertices N(6,1), E(0,-8), M(-4,-4) and O(2,5).

NE is parallel to MO since they have the same slope EM is parallel to NO since they have the same slope NEMO is a parallelogram since both pairs of opp. sides are parallel

The points (-2,4) and (0,-2) lie on line 1, and (-4,0) and (2,2) lie on line 2. Determine if the lines are parallel, perpendicular or neither and explain why.

The lines are perpendicular because their slopes are opposite reciprocals.