To calculate the missing side lengths, perimeter, and area of triangle ABC on the coordinate plane, you'll need the coordinates of the points A, B, and C. Once you have the coordinates, you can follow these steps:
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Finding the side lengths:
- Use the distance formula to find the lengths of sides AB, BC, and AC. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated as: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Calculate:
- Side Length AB: Points A (x₁, y₁) and B (x₂, y₂)
- Side Length BC: Points B (x₂, y₂) and C (x₃, y₃)
- Side Length AC: Points A (x₁, y₁) and C (x₃, y₃)
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Calculate the perimeter:
- The perimeter is the sum of all side lengths: \[ \text{Perimeter} = AB + BC + AC \]
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Calculate the area:
- For the area of a triangle using a base and height: \[ \text{Area} = \frac{1}{2} \times b \times h \]
- Here, \(b\) is the length of base BC and \(h\) is the height from point A to line BC. To find the height, you might need to use the formula for the distance from a point to a line or simply find the perpendicular distance.
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Final answers:
- Write your answers in simplest radical form, if applicable. For example, if you found side lengths like \(\sqrt{8}\), you can simplify it to \(2\sqrt{2}\).
Once you have completed these calculations, insert the values into the given response areas for each side length, perimeter, and area of Triangle ABC. If you provide the coordinates, I can assist you with specific calculations.