Question

question 13(multiple choice worth 1 points) (04.03 mc) segment bd is an altitude of triangle abc. find the area of the triangle

Explanation:

Step1: Determine the base length

Count the horizontal distance from B to D on the grid. B is at x - coordinate - 1 and D is at x - coordinate 2. The length of the base BD is \(|2-(-1)|=3\).

Step2: Determine the height

Count the vertical distance from A to the line containing BD. A is at y - coordinate 1 and the line BD is at y - coordinate 4. The height (the length from A to the line BD) is \(|4 - 1|=3\).

Step3: Use the triangle - area formula

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). Substitute base = 3 and height = 3 into the formula: \(A=\frac{1}{2}\times3\times 3=\frac{9}{2}=4.5\). But, if we consider the vertical distance from C to the line BD. C is at y - coordinate 6 and the line BD is at y - coordinate 4. The height is \(|6 - 4| = 2\), and the base BD is still 3. Using the area formula \(A=\frac{1}{2}\times base\times height=\frac{1}{2}\times3\times2 = 3\). Let's consider the correct way. The base BD has length 3 (from \(x=-1\) to \(x = 2\)) and the height (vertical distance from A to the line BD) is 3 (from \(y = 1\) to \(y=4\)). The area of \(\triangle ABC\) with base BD and height (vertical distance from A to BD) is \(A=\frac{1}{2}\times base\times height\). The base \(BD = 3\) and the height (vertical distance from A to BD) is 5 (from \(y = 1\) to \(y = 6\)). So \(A=\frac{1}{2}\times3\times5 = 7.5\).

Answer:

7.5