Explanation:
The sum of the intercepts cut off by the axis lines X Y equal a, x Y =ar X y = a r square here r = one by two can be explained as follows:

Intercepts on X-axis:
- When the line intersects the X-axis, the value of Y is zero. So, the intercept on the X-axis is simply the point where the line meets the X-axis, denoted as (a, 0).
- Similarly, for the line x = ar, the intercept on the X-axis is (ar, 0).

Intercepts on Y-axis:
- When the line intersects the Y-axis, the value of X is zero. So, the intercept on the Y-axis is the point where the line meets the Y-axis, denoted as (0, a).
- For the line x = a r square, the intercept on the Y-axis is (0, a r square).

Sum of Intercepts:
- The sum of the intercepts on the X-axis for both lines is a + ar = a(1 + r).
- The sum of the intercepts on the Y-axis for both lines is a + a r square = a(1 + r square).

Substitute r = 1/2:
- When r = 1/2, the sum of intercepts on the X-axis becomes a(1 + 1/2) = a(3/2) = (3/2)a.
- Similarly, the sum of intercepts on the Y-axis becomes a(1 + 1/4) = a(5/4) = (5/4)a.
Therefore, the sum of intercepts cut off by the axis lines X Y equal a, x Y =ar X y = a r square when r = 1/2 is 3/2a on the X-axis and 5/4a on the Y-axis.