Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A graphic designer is creating an animation where an object moves from point A(-2, 5) to point B(4, -3). If the object moves along a straight line, what are the coordinates of the midpoint of its path?
- A(1, 1)
- B(6, -8)
- C(2, 2)
- D(3, -4)
Show answer & explanationAnswer & explanation
Correct answer: A. (1, 1)
The midpoint of a line segment connecting two points (x1, y1) and (x2, y2) is found using the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Substitute the coordinates of points A and B into this formula.
Why the other options are wrong
- B. This is incorrect; these are the differences in coordinates, not the midpoint.
- C. This is incorrect; it might be a result of an incorrect sum or division.
- D. This is incorrect; it might be related to subtracting coordinates or incorrect signs.
Midpoint Formula
A formula used to find the coordinates of the point exactly halfway between two given points in a coordinate plane.
- For two points (x1, y1) and (x2, y2).
- Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).
- Essentially averages the x-coordinates and the y-coordinates separately.
Memory trick: Midpoint: 'Average' the 'X's, 'Average' the 'Y's, 'Comma' in between!