91Ó°ÊÓ

Find the area of the triangular region defined by \(y \geqslant 2 x-1\), \(x \geqslant 0, \quad y \leqslant 0\)

The gradient of the line joining \((1,4)\) and \((-2,5)\) is: (a) \(\frac{1}{3}\) (b) \(-\frac{1}{3}\) (c) 3 (d) \(-3\) (e) \(1.3\)

Write down the equation of the line which goes through the point \((7,3)\) and which is inclined at \(45^{\circ}\) to the positive direction of the \(x\)-axis. Find the area enclosed by this line and the coordinate axes.

The gradient of the line perpendicular to the join of \((-1,5)\) and \((2,-3)\) is: (a) \(\frac{3}{8}\) (b) \(-2 \frac{2}{3}\) (c) \(\frac{1}{2}\) (d) 2 (e) \(2 \frac{2}{3}\).

The equations of two adjacent sides of a rhombus are \(y=2 x+4\), \(y=-\frac{1}{3} x+4\). If \((12,0)\) is one vertex and all vertices have positive coordinates, find the coordinates of the other three vertices.