Mathematics
Grade 10
15 min
Midpoint formula
Midpoint formula
What you'll learn
- Identify the commutative, associative, and identity properties of addition in at least 3 out of 4 given examples.
- Solve addition problems using the commutative and associative properties to make calculations easier, demonstrating the correct application of each property in at least 2 out of 3 problems.
- Explain how the identity property of addition (adding zero) works, providing at least two different numerical examples.
- Apply the properties of addition to determine a missing addend in an equation (e.g., 5 + __ = 5), correctly identifying the missing number in at least 4 out of 5 equations.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the midpoint of a line segment in the context of a coordinate plane.
State and correctly write the midpoint formula.
Calculate the coordinates of the midpoint of a line segment given the coordinates of its two endpoints.
Determine the coordinates of an unknown endpoint of a line segment when given the coordinates of the midpoint and the other endpoint.
Apply the midpoint formula to solve problems involving geometric figures such as triangles, parallelograms, and circles.
Use the midpoint formula as a tool in coordinate geometry proofs, such as proving that the diagonals of a parallelogram bisect each other.
Ever tried to meet a friend exactly halfway between your houses? The midpoint formula is the GPS for your geometry problems! 🗺️
In this tutori...
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Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis.The grid system on a map where locations are identified by latitude and longitude.
Line SegmentA part of a line that is bounded by two distinct points, called endpoints.The straight path between point A(1, 2) and point B(5, 6).
EndpointsThe points at the beginning and end of a line segment.For the segment AB, the endpoints are A and B.
MidpointThe point on a line segment that divides it into two equal, congruent segments.If M is the midpoint of segment AB, then the length of AM is equal to the length of MB.
Ordered Pair (x, y)A pair of numbers that represents the coordinates of a point on the coordinate plane, where 'x&#...
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Core Formulas
The Midpoint Formula
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
Use this formula to find the coordinates of the midpoint (M) of a segment with endpoints (x₁, y₁) and (x₂, y₂). It finds the average of the x-coordinates and the average of the y-coordinates.
Finding a Missing Endpoint Formula
x_2 = 2x_m - x_1 \quad \text{and} \quad y_2 = 2y_m - y_1
Use this rearranged version of the formula when you know the midpoint (x_m, y_m) and one endpoint (x₁, y₁), and you need to find the other endpoint (x₂, y₂).
5 more steps in this tutorial
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Challenging
Point M(3, 5) is the midpoint of segment AB. Point N(7, 2) is the midpoint of segment BC. What are the coordinates of the midpoint of segment AC?
A.(5, 3.5)
B.(4, -3)
C.(10, 7)
D.Cannot be determined from the given information.
Challenging
Point B is the midpoint of segment AC. Point C is the midpoint of segment BD. If A is (-9, 5) and C is (-1, 1), what are the coordinates of D?
A.(7, -3)
B.(3.5, -1.5)
C.(-5, 3)
D.(8, -4)
Challenging
In parallelogram PQRS, the coordinates of P, Q, and R are (-2, 1), (1, 5), and (8, 3) respectively. What are the coordinates of vertex S?
A.(5, -1)
B.(11, 7)
C.(5, -1)
D.(4.5, 2)
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Frequently asked questions
What grade level is "Midpoint formula"?
Midpoint formula is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Midpoint formula?
You'll be able to: Identify the commutative, associative, and identity properties of addition in at least 3 out of 4 given examples; Solve addition problems using the commutative and associative properties to make calculations easier….
Is "Midpoint formula" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Midpoint formula?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.