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Find the missing side lengths, perimeter, and area of triangle ABC on the coordinate plane. All answers should be in simplest radical form, if necessary: (5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Side Length AB: Response area Side Length BC: Response area Side Length AC: Response area Perimeter of Triangle ABC: Response area Area of Triangle ABC: Response area Note: the formula for area of a triangle is A=bh2 , where b is the length of the base (BC) and h is the height from side BC to point A.

1 answer

To find the side lengths, perimeter, and area of triangle ABC on the coordinate plane, we need the coordinates of points A, B, and C. Let’s assume you have the coordinates already, such as:

  • A (x1, y1)
  • B (x2, y2)
  • C (x3, y3)

Using those coordinates, we can calculate the distances (side lengths) using the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Side Lengths

  1. Side Length AB: \[ AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

  2. Side Length BC: \[ BC = \sqrt{(x_3 - x_2)^2 + (y_3 - y_2)^2} \]

  3. Side Length AC: \[ AC = \sqrt{(x_3 - x_1)^2 + (y_3 - y_1)^2} \]

Perimeter

The perimeter \( P \) of triangle ABC is simply the sum of all three sides: \[ P = AB + BC + AC \]

Area

To find the area using the given formula \( A = \frac{1}{2}bh \), we first need to determine the height \( h \) from point A to the base BC. If you have the coordinates, you can determine the height with respect to the base.

Alternatively, you can calculate the area using the coordinates of the triangle: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Inputs

  1. Side Length AB: (Insert calculated \( AB \))
  2. Side Length BC: (Insert calculated \( BC \))
  3. Side Length AC: (Insert calculated \( AC \))
  4. Perimeter of Triangle ABC: (Insert calculated \( P \))
  5. Area of Triangle ABC: (Insert calculated area)

Please provide the coordinates of points A, B, and C for specific calculations.