Question

If R (5, 6) is the midpoint of the line segment AB joining the points A (6, 5) and B (4, y), then y equals to

• A. 5
• B. 7
• C. 6
• D. 12

Hint:

The coordinates of the endpoints and the midpoint form an arithmetic progression.
For the y-coordinates: the sequence from \(A\) to \(R\) to \(B\) is \(5 \to 6 \to y\).
Since the step from \(5\) to \(6\) is \(+1\), the next step from \(6\) to \(y\) must also be \(+1\).
Thus, \(y = 6 + 1 = 7\) instantly.

Answer 1

The Correct Option is B

Step 1: Use the symmetry of a midpoint instead of the midpoint formula.
Since $R$ is the midpoint of $AB$, the step from $A$ to $R$ must be exactly the same as the step from $R$ to $B$.
Step 2: Find the step from A to R.
\[ R - A = (5 - 6,\ 6 - 5) = (-1, 1) \]
Step 3: Apply the same step from R to find B.
\[ B = R + (-1, 1) = (5 - 1,\ 6 + 1) = (4, 7) \]
Step 4: Read off y.
Comparing with the given $B(4, y)$, we get $y = 7$.
\[ \boxed{y = 7} \]