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A(a, b) is the coordinates of the intersection between the lines:
(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
A(a, b) is the coordinates of the intersection between the lines:(x + ...
The best answer is E.
There is no need to draw the two lines. Multiply equation (1) by 2 and then add the equations to get:
6x = 7 à x = 7/6, y = -1/6.
Draw a rectangular axis system and mark the point A and B.
Complete the two points to a triangle so one of sides is 3 and the other is 4, the hypotenuse, which is also the requested length is 5.
6x = 7 à x = 7/6, y = -1/6.
Draw a rectangular axis system and mark the point A and B.
Complete the two points to a triangle so one of sides is 3 and the other is 4, the hypotenuse, which is also the requested length is 5.
This question is part of UPSC exam. View all GMAT courses
Most Upvoted Answer
A(a, b) is the coordinates of the intersection between the lines:(x + ...
1) y = mx + n
2) ax + by + c = 0
To find the intersection point, we need to solve the system of equations formed by the two lines.
First, let's find the slope and y-intercept of the first line (y = mx + n).
The slope (m) can be found by comparing the coefficients of x and y:
m = coefficient of x / coefficient of y
= 1 / 1
= 1
The y-intercept (n) can be found by setting x = 0 and solving for y:
y = mx + n
0 = 1(0) + n
n = 0
So, the first line equation becomes:
y = x
Now, let's convert the second line equation (ax + by + c = 0) into slope-intercept form.
ax + by + c = 0
by = -ax - c
y = (-a/b)x - (c/b)
Now we can equate the two equations to find the intersection point:
y = x
y = (-a/b)x - (c/b)
Since both equations are equal to y, we can set them equal to each other:
x = (-a/b)x - (c/b)
Now, let's solve for x:
x + (a/b)x = - (c/b)
(1 + a/b)x = - (c/b)
x = - (c/b) / (1 + a/b)
x = - (c/b) / (b + a) / b)
x = - c / (b(b + a))
Now, substitute this value of x back into either equation to find y:
y = x
y = - c / (b(b + a))
So, the coordinates of the intersection point are:
A(a, b) = (- c / (b(b + a)), - c / (b(b + a)))
2) ax + by + c = 0
To find the intersection point, we need to solve the system of equations formed by the two lines.
First, let's find the slope and y-intercept of the first line (y = mx + n).
The slope (m) can be found by comparing the coefficients of x and y:
m = coefficient of x / coefficient of y
= 1 / 1
= 1
The y-intercept (n) can be found by setting x = 0 and solving for y:
y = mx + n
0 = 1(0) + n
n = 0
So, the first line equation becomes:
y = x
Now, let's convert the second line equation (ax + by + c = 0) into slope-intercept form.
ax + by + c = 0
by = -ax - c
y = (-a/b)x - (c/b)
Now we can equate the two equations to find the intersection point:
y = x
y = (-a/b)x - (c/b)
Since both equations are equal to y, we can set them equal to each other:
x = (-a/b)x - (c/b)
Now, let's solve for x:
x + (a/b)x = - (c/b)
(1 + a/b)x = - (c/b)
x = - (c/b) / (1 + a/b)
x = - (c/b) / (b + a) / b)
x = - c / (b(b + a))
Now, substitute this value of x back into either equation to find y:
y = x
y = - c / (b(b + a))
So, the coordinates of the intersection point are:
A(a, b) = (- c / (b(b + a)), - c / (b(b + a)))
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A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer?
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A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer?.
A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A(a, b) is the coordinates of the intersection between the lines:(x + y –1 = 0) and (4x – 2y = 5). What is the shortest distance between A(a, b) and the coordinate B(25/6, 23/6)?a)1b)2c)3d)4e)5Correct answer is option 'E'. Can you explain this answer?.
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