Question

One side of an isosceles triangle is shown on the graph.

The triangle has an area of 12 square units.

Complete the construction of the isosceles triangle by drawing the other two sides of the triangle.

Answer 1

To complete the construction of an isosceles triangle with one base side shown on a graph and an area of 12 square units, follow these general steps:

1. **Identify the base**: Locate the endpoints of the base of the isosceles triangle on the graph. Let’s assume the base runs from point A to point B.

2. **Determine the length of the base (AB)**: Measure the distance between points A and B. Let’s denote this length as \( b \).

3. **Calculate the height (h)**: The area of a triangle is given by the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Given that the area is 12 square units:
\[
12 = \frac{1}{2} \times b \times h
\]
Rearranging gives:
\[
h = \frac{24}{b}
\]

4. **Find the midpoint of the base (M)**: Calculate the midpoint M of base AB, which can be done by averaging the x-coordinates and the y-coordinates of points A and B.

5. **Draw the height**: From point M, measure a vertical distance equal to the height \( h \). This could be either up (to point C) or down (to point C'). Thus, the coordinates of point C will be:
- If going up: \( M_x, M_y + h \)
- If going down: \( M_x, M_y - h \)

6. **Connect the points**: Draw line segments AC and BC (or AC' and BC' if you are going down) to form the other two sides of the triangle.

At this point, you will have a completed isosceles triangle with the area specified, and you can verify by checking that the area calculated matches the area needed.

Make sure to sketch this out on graph paper or a digital graphing tool to ensure accuracy!