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Co-ordinate Geo

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Co-ordinate Geo

by beater » Mon Oct 13, 2008 1:59 pm
In the rectangular coordinate system, a line passes through the points (0,5) and (7,0). Which of the following points must the line also pass through?
A. (-14, 10)
B. (-7, 5)
C. (12, -4)
D. (14, -5)
E. (21, -9)
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Co-ordinate Geo : Answer is D

by oza_gautam » Mon Oct 13, 2008 2:49 pm
D : (14, -5)

Slope for a line : m = (y1-y2) / (x1-x2)
Equation for a line using Slope and Y intercept : Y = m*X + b

(x1,y1) = (0,5)
(x2,y2) = (7,0)

slope of the line given in this example = -(5/7)
Equation of line using first point for Y intercept --> Y = -(5/7)*x + 5

Now try solving this equation for all the points given in the problem.. The answer will be D.

Hint: A and B can be easily crossed out as possible answer if you first plot the line on paper. -14 and -7 will never be valid X-intercepts for this line.
Gautam
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by DeepakR » Tue Oct 14, 2008 8:22 am
The other alternative to what Gautam mentioned is as follows:

Equation of the line is given in 2 point form as:

(y-y1)/(y2-y1)=(x-x1)/(x2-x1). This will give the eqn of that line passing thru the 2 points. If any point lies on a line it has to satisfy the eqn of the line. So substitute the answer choices in the above eqn we found out and hence answer shud be D

- Deepak
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by 2009wish » Sat Oct 18, 2008 9:43 am
a direct approach is using the intercept formula :

x/ a + y/b= 1 (where a and b are the intercepts on x and y axis)

we get the equation as-- 5x +7y= 35

susbtituting the answer choices ..... we have D as the answer
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by anniev2 » Wed Mar 11, 2009 8:54 am
here is the official explanation from MGMAT:

Use slope formula to find slope is equal to -5/7

Because we know the line passes through (0,5) we have our y-intercept which is 5.

Putting these two pieces of information into the slope-intercept equation gives us y = (-5/7)x + 5. Now all we have to do is plug in the x-coordinate of each of the answer choices and see which one gives us the y-coordinate.

(A) (-14, 10)
y = -5/7(-14) + 5 = 15; this does not match the given y-coordinate.

(B) (-7, 5)
y = -5/7(-7) + 5 = 10; this does not match the given y-coordinate.

(C) (12, -4)
y = -5/7(12) + 5 = -60/7 + 5, which will not equal an integer; this does not match the given y-coordinate.

(D) (14, -5)
y = -5/7(14) + 5 = -5; this matches the given y-coordinate so we have found our answer.

(E) (21, -9)
y = -5/7(21) + 5 = -15/7 + 5, which will not equal an integer; this does not match the given y-coordinate. (Note that you do not have to test this answer choice if you've already discovered that D works.)

The correct answer is D.


Here is my question:

What if I decided to use the other point that the problem indicates that the line passes through (7, 0) here are the results from plugging the X value in the slope equation.

A: (-14, 10)
y = -5/7 x -14 + 0
y = 10
OK

(B) (-7, 5)
y = -5/7 x -7 + 0
y=5
OK

(C) (12, -4)
y = -5/7 x 12 + 0
y= non integer
NOT OK

(D) (14, -5)
y = -5/7 x -14 + 0
y= -10
NOT OK (not equal to y intercept in points given)

(E) (21, -9)
y = -5/7 x 21 + 0
y=15
NOT OK(not equal to y intercept in points given)

With this info, how can I tell which is the correct answer by using the answer choices???
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