A straight line through the point A (3,4) is such that its intercept between the axis is bisected at A then its equation is : A. `x+y=7` B. `3x-4y+7=0 ` C. ` 4x+3y=24` D. `3x+4y=24`

Explanation

To find the equation of the straight line that passes through the point A(3, 4) and has its intercepts on the axes bisected at point A, we can follow these steps:

### Step 1: Understand the Intercepts
Let the x-intercept be P(α, 0) and the y-intercept be Q(0, β). The line will intercept the x-axis at point P and the y-axis at point Q.

### Step 2: Use the Midpoint Formula
Since point A(3, 4) bisects the segment PQ, we can use the midpoint formula. The midpoint M of a segment with endpoints (x1, y1) and (x2, y2) is given by:
\[
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