Math · Coordinate Geometry
Midpoint of a Segment
Medium
Math
Coordinate Geometry
Question
What is the midpoint of the segment with endpoints (6, 6) and (-2, -2)?
Answer choices
- (8, 8)
- (2, 3)
- (4, 4)
- (2, 2)
- (3, 2)
D Correct answer: D) (2, 2)
Set up the problem carefully before computing. Average the x-coordinates and the y-coordinates separately.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Midpoint = ((x1+x2)/2, (y1+y2)/2) = ((6+-2)/2, (6+-2)/2) = (2, 2).
Why each wrong answer is wrong
- A) (8, 8): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) (2, 3): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) (4, 4): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) (3, 2): A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Midpoint = average of the x-coordinates, average of the y-coordinates. It is just two arithmetic averages.
More Medium Coordinate Geometry
- Slope Between Two PointsWhat is the slope of the line passing through (2, 4) and (5, 6)?
- Distance Between Two PointsWhat is the distance between (1, 2) and (5, 6)?
- Equation of a Line in Slope-Intercept FormA line has slope 3 and y-intercept 1. Write its equation in slope-intercept form.
- Slope Between Two PointsWhat is the slope of the line passing through (1, -1) and (5, 1)?
- Distance Between Two PointsWhat is the distance between (2, 0) and (6, 4)?