Math Problem Statement
Solution
The problem you've shared is asking for the following:
Given:
In a coordinate system , with a unit scale where 1 cm represents 1 unit, the points , , and are provided.
Questions:
- A) Write down the coordinates of points , , and .
- B) Write down the coordinates of point , which is symmetric to point with respect to the origin.
- C) Find the area of triangle .
Let's solve these step by step:
A) Coordinates of points , , and :
From the grid in the image, it looks like the coordinates are:
B) Coordinates of point :
Point is symmetric to with respect to the origin. The coordinates of are the negation of the coordinates of . Hence, if , then:
C) Area of triangle :
We can calculate the area of triangle using the formula for the area of a triangle with given vertices , , and :
Substituting , , and :
Summary of answers:
- A) , ,
- B)
- C) Area of triangle is square units
Would you like more details or have further questions?
Follow-up questions:
- What is the formula for finding the area of a triangle given its vertices in the coordinate plane?
- Can you explain why the coordinates of are the negation of 's coordinates?
- How would the area change if was at a different point?
- Can you compute the perimeter of triangle ?
- How does symmetry help when reflecting points across the origin?
Tip: To reflect a point across the origin, just negate both the x- and y-coordinates of the point.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Symmetry
Area of a Triangle
Formulas
Symmetry across the origin: (x, y) -> (-x, -y)
Area of triangle given vertices: A = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Theorems
Symmetry Theorem
Triangle Area Formula
Suitable Grade Level
Grades 7-9
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