Math · Coordinate Geometry
Distance Between Two Points
Medium
Math
Coordinate Geometry
Question
What is the distance between (1, 2) and (5, 6)?
Answer choices
- 8
- 6.6568542494924
- 0
- 4.6568542494924
- 5.6568542494924
E Correct answer: E) 5.6568542494924
Set up the problem carefully before computing. Distance formula is the Pythagorean theorem applied to coordinate differences.
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
Distance = √((x2-x1)^2 + (y2-y1)^2) = √(4^2 + 4^2) = √(16 + 16) = √32 = 5.6568542494924.
Why each wrong answer is wrong
- A) 8: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) 6.6568542494924: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 0: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 4.6568542494924: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Distance formula = √(Δx² + Δy²). It is just the Pythagorean theorem. The 3-4-5 and 5-12-13 triangles show up constantly.
More Medium Coordinate Geometry
- Slope Between Two PointsWhat is the slope of the line passing through (2, 4) and (5, 6)?
- Midpoint of a SegmentWhat is the midpoint of the segment with endpoints (6, 6) and (-2, -2)?
- 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)?