In Figure PQRS is a square. What is the slope of segment QR ?

Options

A. `-(10)/(3)`
B. `-(7)/(3)`
C. `-(4)/(3)`
D. `(3)/(7)`

Answer

B

Explanation

The slope m of a line that goes through the points `(x_(1), y_(1))` and `(x_(2),y_(2))` is given by `m = (y_(2)-y_(1))/(x_(2)-x_(1))`. The slope of PQ is `(10-7)/(7-0)=(3)/(7)`. Since PQRS is a square, QR is perpendicular to PQ. When two lines are perpendicular and the lines are not parallel to the coordinate axes (the coordinate axes are the x - axis and the y - axis), the slopes of the lines are negative reciprocals. Since QR is perpendicular to PQ, the slope of QR is the negative reciprocal of the slope of PQ . The slope of QR is `(-1)/(((3)/(7)))`, which is `-(7)/(3)`.