Mathematics
Grade 10
15 min
Area and perimeter in the coordinate plane: Set 2
Area and perimeter in the coordinate plane: Set 2
What you'll learn
- Identify the ratio of two quantities from a given word problem with at least 80% accuracy.
- Write a ratio in three different ways (a to b, a:b, a/b) to represent the same relationship, given a real-world scenario.
- Solve problems involving ratios using visual models (e.g., tape diagrams, double number lines) and explain the solution process.
- Explain, in your own words, what a ratio is and how it compares two quantities, providing at least two different examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the perimeter of complex polygons using the Distance Formula.
Determine the area of any simple polygon using the Shoelace Formula.
Find the area of composite figures by decomposing them into simpler shapes like triangles and rectangles.
Apply the 'boxing-in' method to find the area of non-standard polygons.
Verify properties of geometric figures using coordinate geometry formulas before calculating area and perimeter.
Solve multi-step problems involving area and perimeter on the coordinate plane.
Ever wondered how a GPS calculates the area of a park or a property lot just from its corner coordinates? 🗺️ Let's learn the powerful geometry behind it!
This tutorial moves beyond simple squares and focuses on complex and composite shap...
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Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PolygonA polygon whose vertices are defined by ordered pairs (x, y) in the Cartesian coordinate plane.A triangle with vertices at A(1, 2), B(5, 6), and C(3, -1).
Distance FormulaA formula derived from the Pythagorean theorem used to find the straight-line distance between two points in the coordinate plane.The distance between (2, 3) and (5, 7) is sqrt((5-2)^2 + (7-3)^2) = sqrt(3^2 + 4^2) = sqrt(25) = 5 units.
Shoelace FormulaA method to calculate the area of any simple polygon given the coordinates of its vertices in order.For a triangle with vertices (x1, y1), (x2, y2), (x3, y3), the area is 0.5 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|.
Decomposition MethodThe process of finding the area of a complex polygon by breaking it down into simpler, non-o...
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Core Formulas
The Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Use this formula to find the length of any segment in the coordinate plane, which is essential for calculating the perimeter of a polygon. (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints.
The Shoelace Formula
Area = \frac{1}{2} |(x_1y_2 + x_2y_3 + ... + x_ny_1) - (y_1x_2 + y_2x_3 + ... + y_nx_1)|
A powerful formula for finding the area of any simple polygon. List the n vertices (x₁, y₁), ..., (xₙ, yₙ) in counter-clockwise order and repeat the first vertex at the end. Sum the products of the downward diagonals and subtract the sum of the products of the upward diagonals.
Area of a Triangle (Coordinate Method)
Area = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|
This is a simp...
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Challenging
Three vertices of a parallelogram ABCD are A(1, 1), B(5, 2), and C(6, 5). Which of the following are possible coordinates for the fourth vertex, D?
A.(3, 3)
B.(2, 4)
C.(0, 5)
D.(4, -2)
Challenging
A triangle with vertices A(1, 4), B(5, 2), and C(k, 6) has an area of 10 square units. Which of the following is a possible value for k?
A.3
B.5
C.-10
D.7
Challenging
A rectangular park is defined by vertices R(0,0), S(10,0), T(10,8), and U(0,8). A triangular garden with vertices P(2,2), Q(8,2), and M(5,6) is built inside the park. What is the area of the park that is NOT covered by the garden?
A.80 square units
B.12 square units
C.68 square units
D.92 square units
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What grade level is "Area and perimeter in the coordinate plane: Set 2"?
Area and perimeter in the coordinate plane: Set 2 is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area and perimeter in the coordinate plane: Set 2?
You'll be able to: Identify the ratio of two quantities from a given word problem with at least 80% accuracy; Write a ratio in three different ways (a to b, a:b, a/b) to represent the same relationship, given a real-world scenario; Solve problems….
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This lesson includes 31 practice questions across multiple difficulty levels, each with instant feedback and explanations.