Question

question 2 (multiple choice worth 1 points) (04.03 hc) right triangle abc is on a coordinate plane. segment ab is on the line y = 2 and is 6 units long. point c is on the line x = -3. what is the y - value of point c if the area of δabc is 9 units squared? options: 5, 6, 7, 8

Explanation:

Answer:

To solve for the \( y \)-value of point \( C \):

1. Recall the area formula for a triangle: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
2. Here, \( AB \) (length 6) is the base. Let the height be the vertical distance from \( C \) to the line \( y = 2 \) (since \( AB \) is horizontal, the height is vertical).
3. Substitute into the area formula: \( 9 = \frac{1}{2} \times 6 \times \text{height} \).
4. Solve for height: \( 9 = 3 \times \text{height} \implies \text{height} = 3 \).
5. Point \( C \) is on \( x = -3 \). The vertical distance from \( C \) to \( y = 2 \) is 3, so the \( y \)-value of \( C \) is \( 2 + 3 = 5 \) or \( 2 - 3 = -1 \). However, from the answer choices (5, 6, 7, 8), the correct \( y \)-value is \( 5 \) (assuming the triangle is above \( y = 2 \); if below, \( -1 \) is not an option here).

Final answer: \( \boldsymbol{5} \) (matching the first option).