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The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?
- a)(–4, 1)
- b)(–2, 2)
- c)(0, 1)
- d)(0, –1)
- e)(2, 0)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The line represented by the equation y = 4 – 2x is the perpendic...
First, rewrite the line y=4-2x as y=-2x+4 . The equation is now in the form y=mx+b where m represents the slope and b represents the y-intercept. Thus, the slope of this line is -2.
By definition, if line F is the perpendicular bisector of line G, the slope of line F is the negative inverse of the slope of line G. Since we are told that the line
y=-2x+4 is the perpendicular bisector of line segment RP, line segment RP must have a slope of 1/2 (which is the negative inverse of ).
Now we know that the slope of the line containing segment RP is 1/2 but we do not know its y-intercept. We can write the equation of this line as
where b represents the unknown y-intercept.
By definition, if line F is the perpendicular bisector of line G, the slope of line F is the negative inverse of the slope of line G. Since we are told that the line
y=-2x+4 is the perpendicular bisector of line segment RP, line segment RP must have a slope of 1/2 (which is the negative inverse of ).
Now we know that the slope of the line containing segment RP is 1/2 but we do not know its y-intercept. We can write the equation of this line as
where b represents the unknown y-intercept.To solve for b, we can use the given information that the coordinates of point R are (4, 1). Since point R is on the line 
we can plug 4 in for x and 1 in for y as follows:
Now we have a complete equation for the line containing segment RP:
We also have the equation of the perpendicular bisector of this line: y=-2x+4. To determine the point M at which these two lines intersect, we can set these two equations to equal each other as follows:
Thus, the intersection point M has x-coordinate 2. Using this value, we can find the y coordinate of point M:
y=-2x+4
y=-2(2)+4
y=0
Thus the perpendicular bisector intersects line segment RP at point M, which has the coordinates (2, 0). Since point M is on the bisector of RP, point M represents the midpoint on line segment RP; this means that it is equidistant from point R and point P.
We know point R has an x-coordinate of 4. This is two units away from the x-coordinate of midpoint M, 2. Therefore the x-coordinate of point P must also be two units away from 2, which is 0.
We know point R has a y-coordinate of 1. This is one unit away from the y-coordinate of midpoint M, 0. Therefore, the y-coordinate of point P must also be one unit away from 0, which is –1.
The coordinates of point P are
(0,-1). The correct answer is D.
we can plug 4 in for x and 1 in for y as follows:Now we have a complete equation for the line containing segment RP:
We also have the equation of the perpendicular bisector of this line: y=-2x+4. To determine the point M at which these two lines intersect, we can set these two equations to equal each other as follows:
Thus, the intersection point M has x-coordinate 2. Using this value, we can find the y coordinate of point M:
y=-2x+4
y=-2(2)+4
y=0
Thus the perpendicular bisector intersects line segment RP at point M, which has the coordinates (2, 0). Since point M is on the bisector of RP, point M represents the midpoint on line segment RP; this means that it is equidistant from point R and point P.
We know point R has an x-coordinate of 4. This is two units away from the x-coordinate of midpoint M, 2. Therefore the x-coordinate of point P must also be two units away from 2, which is 0.
We know point R has a y-coordinate of 1. This is one unit away from the y-coordinate of midpoint M, 0. Therefore, the y-coordinate of point P must also be one unit away from 0, which is –1.
The coordinates of point P are
(0,-1). The correct answer is D.
Most Upvoted Answer
The line represented by the equation y = 4 – 2x is the perpendic...
The line represented by the equation y = 4 is a horizontal line that passes through the point (0, 4) on the y-axis. This line has a constant y-coordinate of 4 for all values of x.
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The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?a)(–4, 1)b)(–2, 2)c)(0, 1)d)(0, –1)e)(2, 0)Correct answer is option 'D'. Can you explain this answer?
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The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?a)(–4, 1)b)(–2, 2)c)(0, 1)d)(0, –1)e)(2, 0)Correct answer is option 'D'. 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 The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?a)(–4, 1)b)(–2, 2)c)(0, 1)d)(0, –1)e)(2, 0)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?a)(–4, 1)b)(–2, 2)c)(0, 1)d)(0, –1)e)(2, 0)Correct answer is option 'D'. Can you explain this answer?.
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