91Ó°ÊÓ

In Exercises 1 through 6, plot the given point \(P\) and such of the following points as may apply: (a) The point \(Q\) such that the line through \(Q\) and \(P\) is perpendicular to the \(x\) axis and is bisected by it. Give the coordinates of \(Q\). (b) The point \(R\) such that the line through \(P\) and \(R\) is perpendicular to and is bisected by the \(y\) axis. Give the coordinates of \(R\). (c) The point \(S\) such that the line through \(P\) and \(S\) is bisected by the origin. Give the coordinates of \(S\). (d) The point \(T\) such that the line through \(P\) and \(T\) is perpendicular to and is bisected by the \(45^{\circ}\) line through the origin bisecting the first and third quadrants. Give the coordinates of \(T\). $$ P(1,-2) $$

Given \(F(x)=\sqrt{2 x+3}\), find: (a) \(F(-1)\) (b) \(F(4)\) (c) \(F\left(\frac{t}{2}\right)\) (d) \(F(30)\) (e) \(F(2 x+3)\) (f) \(\frac{F(x+h)-F(x)}{h}, h \neq 0\)

In Exercises 1 through 6, plot the given point \(P\) and such of the following points as may apply: (a) The point \(Q\) such that the line through \(Q\) and \(P\) is perpendicular to the \(x\) axis and is bisected by it. Give the coordinates of \(Q\). (b) The point \(R\) such that the line through \(P\) and \(R\) is perpendicular to and is bisected by the \(y\) axis. Give the coordinates of \(R\). (c) The point \(S\) such that the line through \(P\) and \(S\) is bisected by the origin. Give the coordinates of \(S\). (d) The point \(T\) such that the line through \(P\) and \(T\) is perpendicular to and is bisected by the \(45^{\circ}\) line through the origin bisecting the first and third quadrants. Give the coordinates of \(T\). $$ P(2,2) $$

In Exercises 1 through 4 , find the slope of the line through the given points. $$ (-2.1,0.3),(2.3,1.4) $$

In Exercises 1 through 6, plot the given point \(P\) and such of the following points as may apply: (a) The point \(Q\) such that the line through \(Q\) and \(P\) is perpendicular to the \(x\) axis and is bisected by it. Give the coordinates of \(Q\). (b) The point \(R\) such that the line through \(P\) and \(R\) is perpendicular to and is bisected by the \(y\) axis. Give the coordinates of \(R\). (c) The point \(S\) such that the line through \(P\) and \(S\) is bisected by the origin. Give the coordinates of \(S\). (d) The point \(T\) such that the line through \(P\) and \(T\) is perpendicular to and is bisected by the \(45^{\circ}\) line through the origin bisecting the first and third quadrants. Give the coordinates of \(T\). $$ P(-2,-2) $$

Find the midpoints of the diagonals of the quadrilateral whose vertices are \((0,0),(0,4),(3,5)\), and \((3,1)\).

In Exercises 1 through 10, solve for \(x\). $$ |x-2|=|3-2 x| $$

In Exercises 1 through 6, plot the given point \(P\) and such of the following points as may apply: (a) The point \(Q\) such that the line through \(Q\) and \(P\) is perpendicular to the \(x\) axis and is bisected by it. Give the coordinates of \(Q\). (b) The point \(R\) such that the line through \(P\) and \(R\) is perpendicular to and is bisected by the \(y\) axis. Give the coordinates of \(R\). (c) The point \(S\) such that the line through \(P\) and \(S\) is bisected by the origin. Give the coordinates of \(S\). (d) The point \(T\) such that the line through \(P\) and \(T\) is perpendicular to and is bisected by the \(45^{\circ}\) line through the origin bisecting the first and third quadrants. Give the coordinates of \(T\). $$ P(0,-3) $$

In Exercises 5 through 10, find an equation of the circle satisfying the given conditions. Center is at \((-2,5)\) and tangent to the line \(x=7\).

In Exercises 7 through 12, the functions \(f\) and \(g\) are defined. In each problem define the following functions and determine the domain of the resulting function: (a) \(f+g ;\) (b) \(f-g ;\) (c) \(f \cdot g ;\) (d) \(f / g ;\) (e) \(g / f\); (f) \(f \circ g ;(\mathrm{g}) g \circ f\). $$ f(x)=x-5 ; g(x)=x^{2}-1 $$