Question

C is the mid-point of PQ, if P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are

• A. -6 and 1
• B. -6 and 2
• C. 6 and -1
• D. 6 and -2

Answer 1

The Correct Option is A

The problem states that C is the midpoint of line segment PQ. By definition, the midpoint of a line segment with endpoints \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) is given by:

\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

Here, \(P(4, x)\), \(C(y, -1)\), and \(Q(-2, 4)\). Setting up equations from the midpoint formula, we have:

1. \( \frac{4 + (-2)}{2} = y \)

2. \( \frac{x + 4}{2} = -1 \)

Now solving each equation:

For equation 1:

\[ y = \frac{4 - 2}{2} = \frac{2}{2} = 1 \]

For equation 2:

\[ \frac{x + 4}{2} = -1 \]

Multiply both sides by 2:

\[ x + 4 = -2 \]

Subtract 4 from both sides:

\[ x = -6 \]

Thus, the values of \( x \) and \( y \) are -6 and 1, respectively. Therefore, the correct answer is -6 and 1.