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geometry help pls

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

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I believe this is a geometry problem. You should not use algebra to solve it.

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3 Answers

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.
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.
 
 
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.
 
 
 
 
 

Comments

My mistake.  It is (c).  I apologize.
You had the right answer, it just wasn't reduced.  You do so much great work on the site.  Thanks for the confirmation.  God bless.

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