Florida B.E.S.T. MA.912.NSO.2.3
The Standard
Calculate the distance and midpoint between two numbers on the complex coordinate plane.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students treat a + bi as the point (a, b) on the complex plane. They use coordinate differences and the Pythagorean theorem for distance. They average the real parts and imaginary parts separately for the midpoint.
What Mastery Looks Like
- Given two complex numbers, a student plots both points correctly and finds the exact distance, including simplified radicals when needed. The student writes the midpoint in a + bi form and verifies that it lies halfway between the endpoints.
Common Misconceptions
- Students may place the imaginary part on the horizontal axis or ignore its sign. Some add coordinate differences instead of using the Pythagorean theorem. Others divide the distance by two rather than averaging corresponding coordinates to find the midpoint.
How to Assess It
- Exit ticket: Let z₁ = -3 + 4i and z₂ = 5 - 2i. Plot both numbers, then find their exact distance and midpoint.
Lesson moves
Ways to Teach It
Plot 1 + 2i and 5 - i on graph paper, measure the segment with string, then verify its length using calculation.
Write an explanation of why averaging the real parts and averaging the imaginary parts gives the midpoint.
Match cards showing pairs of complex numbers with cards showing their distances and midpoints, then check each match by calculation.
Model two drone locations with complex numbers, then calculate their separation and the coordinates of a meeting point.
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Related Standards
- MA.912.NSO.2.5
Represent complex numbers on the complex plane in rectangular and polar forms.
- MA.912.NSO.2.4
Solve mathematical and real-world problems involving complex numbers represented algebraically or on the coordinate plane.
- MA.8.GR.1.2
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
- MA.6.GR.1.2
Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane.
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