geometry help pls

Question

Points (6, 9) and (-4, -6) form a line. This line is parallel to a second line containing the point (-3, 2). Which of the following points would fall on this line to make the two lines parallel?



A: (12, -8) Strike Reset
B: (12, 4) Strike Reset
C: (3, 11) Strike Reset
D: (-2, -3) Strike Reset

Answer 1

m = 3/2 (established by other tutors)

 

Pt-slope formula using m = 3/2 and pt (-3, 2):

 

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

 

y = (3/2)x + 9/2 + 2

 

y = (3/2)x + 13/2

 

(3, 11) is on the line y = (3/2)x + 13/2?

 

(3/2)(3) + 13/2 = 9/2 + 13/2 = 22/2 = 11

 

 

Vivian had the right answer in a way for c).  9/6 = 3/2 when reduced.

 

 

Hope this helps.

 

 

Answer 2

Just using geometry:

Form a right triangle by dropping a line from point (6.9) down to (6,-6) and a line from (-4,-6) to (6,-6).

Let A = (6,9)

Let B = (-4,-6), and

Let C = (6,-6)

 

Line AC has a length of 15 and line BC has a length of 10.

Calculate the tangent of angle ∠ABC. Opposite over adjacent.

 

Create a triangle ΔDEF that is congruent to ΔABC with the given point (-3,2) as point E of the new triangle and side DE parallel to side AB. Extend the line DE out in each direction. The answer must lie on this line.

At this point I would plot all four answers. One of these will fall on the extended line DE.

Check it by comparing the difference between the y's of the answer and point (-3,2) divided by the difference of the x's of the answer and point (-3,2). That should be equal to the tangent calculated.

Answer C (3,11) lies on the line DE.

To check take (11-2)/(3-(-3)) = 9/6 = 3/2.

Answer 3

Hi Michelle;

Primary line...(6, 9) and (-4, -6)

Parallel line...(-3, 2)

 

Our first priority would be to establish the slope for the primary line.

m=slope=(y₂-y₁)/(x₂-x₁)

m=(-6-9)/(-4-6)=-15/-10=3/2

 

The slope of 3/2 is all we need.

The parallel line must have the same slope.

Here is the point we are provided; (-3, 2).

(y₂-y₁)/(x₂-x₁)=3/2

(y₂-2)/(x₂--3)=3/2

(y₂-2)(x₂+3)=3/2

 

A: (12, -8)

Does (-8-2)/(12+3)=3/2?

-10/15=-2/3 does not.

HOWEVER, IF YOU ARE LOOKING FOR THE PERPENDICULAR LINE, THIS IS IT!!!

B: (12, 4)

Does (4-2)/(12+3)=3/2?

2/15 does not.

C: (3, 11)

Does (11-2)/(3+3)=3/2?

9/6 does not.

 

D: (-2, -3)

Does (-3-2)/(-2+3)=3/2

-5/1 does not.