Clash of the coordinates!
A right triangle has to be constructed with the legs parallel to the axes of co-ordinates. If the equations of the medians to the two legs are
and
, the number of values of
for which, such a triangle exists can be expressed as a positive integer
. Enter the value of
as your answer.
The answer is 2.
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1 solution
Let B and H be the base and height of the triangle.
Of the two given lines, one has slope 3 and the other has slope m. The triangle has a vertical and a horizontal side.
The median with slope 3 will either meet the vertical side (height) of the horizontal side (base).
Case I - it meets the base at midpoint. So s l o p e = 3 = B / 2 H So line with slope m must meet the vertical side and m = B H / 2 = 4 3
Case II - The reverse of the above, so m will be four times, instead of one fourth of 3. So m = 12