Question

Line j passes through the points (0, 0) and (c, d). Line k passes through the points (0, 0) and (-d, c). Lines j and k are parallel.

1.True
2.False

Answer 1

Lines j and k are parallel if and only if d = -c.

Step-by-step explanation:

Lines j and k are parallel if their slopes are equal. The slope of line j can be found using the formula:

slope = (rise)/(run) = (d-0)/(c-0) = d/c.

The slope of line k can be found in a similar manner:

slope_k = (c-0)/(-d-0) = -c/d.

In order for lines j and k to be parallel, their slopes must be equal, so d/c = -c/d. This equation can be rearranged to retrieve cd = -c^2, which simplifies to c(d+c) = 0. Since division by zero is undefined, c cannot be equal to 0, so the only solution is d+c = 0. Therefore, lines j and k are parallel if and only if d = -c.