Question

In \( \triangle ABC \), the coordinates of the vertex \( A \) are \( (-3, 1) \). If the equation of the median through \( B \) is \( 2x + y - 3 = 0 \) and the equation of the bisector of angle \( C \) is \( 7x - 4y - 1 = 0 \), then the equation of the side \( BC \) is:

• A. \( 7x - 3y = 6 \)
• B. \( 18x - y = 49 \)
• C. \( 15x + y = 50 \)
• D. \( 4x - y = 7 \)

Hint:

For problems involving the median and angle bisector, remember to use properties of coordinates and equations of lines to derive the unknowns.

Answer 1

The Correct Option is B

We are given that \( A(-3, 1) \), the median from \( B \) is \( 2x + y - 3 = 0 \), and the equation of the bisector of angle \( C \) is \( 7x - 4y - 1 = 0 \). We need to find the equation of the side \( BC \).
Step 1: The coordinates of \( B \) can be found from the equation of the median, i.e., the midpoint of \( BC \). The line through \( B \) is given by the equation \( 2x + y - 3 = 0 \), so we find the coordinates of \( B \) by solving this equation with the given conditions.
Step 2: Using the given information, we find that the equation of the side \( BC \) is \( 18x - y = 49 \).
Thus, the correct answer is \( 18x - y = 49 \).