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North CarolinaMaths

Coordinate Geometry and Reasoning

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you use coordinates to prove a figure is a particular shape?

Use coordinates to prove simple geometric facts about triangles and quadrilaterals using slope and distance (NC.M1.G-GPE.4).
An NC Math 1 EOC answer on coordinate proofs (NC.M1.G-GPE.4): using slope to show sides are parallel or perpendicular and the distance formula to show sides are congruent, to classify triangles and quadrilaterals.
11 min answer →

How do you find the distance between two points, and why does the formula come from the Pythagorean theorem?

Use the distance formula to find the length of a segment and apply it to coordinate problems (NC.M1.G-GPE.4).
An NC Math 1 EOC answer on the distance formula (NC.M1.G-GPE.4): computing the distance between two points, why it follows from the Pythagorean theorem, simplifying radical answers, and using it for congruence.
10 min answer →

How do you find the midpoint of a segment, and how is it used in coordinate problems?

Find the midpoint of a segment and apply it to coordinate problems and figures (NC.M1.G-GPE.6, G-GPE.4).
An NC Math 1 EOC answer on the midpoint formula (NC.M1.G-GPE.6, G-GPE.4): averaging the coordinates, finding an endpoint from the midpoint, and using midpoints in coordinate proofs about figures.
9 min answer →

How do slopes tell you whether two lines are parallel or perpendicular?

Use slope criteria to determine whether lines are parallel, perpendicular, or neither, and write equations of such lines (NC.M1.G-GPE.5).
An NC Math 1 EOC answer on slope criteria (NC.M1.G-GPE.5): equal slopes for parallel lines, negative reciprocal slopes for perpendicular lines, and writing the equation of a line parallel or perpendicular to a given one.
10 min answer →

How do you find the point that divides a segment in a given ratio?

Find the point on a directed line segment that partitions it in a given ratio (NC.M1.G-GPE.6).
An NC Math 1 EOC answer on partitioning a segment (NC.M1.G-GPE.6): finding the point that divides a directed segment in a given ratio using the section method, and why the midpoint is the 1 to 1 case.
10 min answer →