A (3,-1), B (0,0) and C (-3,k) are the vertices of a right-angled triangle with right angle at B. Find the value of k.

Answer 1

To find the value of k, we need to determine the slope of line segment BC and find where it intersects the y-axis.
The slope of line segment BC is given by (change in y ÷ change in x) = (k - 0) ÷ (-3 - 0) = k/(-3).
Since line segment BC is perpendicular to line segment AB (the hypotenuse), the product of their slopes is -1.
So, the slope of line segment AB is the negative reciprocal of the slope of line segment BC.
The slope of line segment AB is given by (-1 - 0) ÷ (3 - 0) = -1/3.
Hence, the slope of line segment BC is the negative reciprocal of -1/3, which is 3.
Now we have: k/(-3) × 3 = -1.
=> k/(-1) = -1.
=> k = 1.
Therefore, the value of k is 1.