91Ó°ÊÓ

Which point(s) lie in the plane \(2 x+y-z=10 ?\) a) \((0,0,10)\) b) \((5,3,-3)\) c) \((2,4,-2)\) d) \((-3,6,-10)\)

Draw an ideally placed figure in the coordinate system; then name the coordinates of each vertex of the figure. a) A trapezoid b) A trapezoid (midpoints of sides are needed)

Apply the Midpoint Formula. A circle has its center at the point \((-2,3) .\) If one endpoint of a diameter is at \((3,-5),\) find the other endpoint of the diameter.

Find an equation of the line described. Leave the solution in the form \(A x+B y=C\). The line contains \((2,-3)\) and is perpendicular to the line \(2 x-3 y=6\)

In Exercises 21 to \(24,\) state whether the lines are parallel, perpendicular, the same (coincident), or none of these. $$2 x+3 y=6 \text { and } 3 x-2 y=12$$

Find an equation of the line described. Leave the solution in the form \(A x+B y=C\). The line is the perpendicular bisector of the line segment that joins \((3,5)\) and \((5,-1)\)

In Exercises 23 to \(26,\) find an equation for each sphere. With center \((0,0,0)\) and radius length \(r=5\)

Apply the Midpoint Formula. A rectangle \(A B C D\) has three of its vertices at \(A(2,-1)\) \(B(6,-1),\) and \(C(6,3) .\) Find the fourth vertex \(D\) and the area of rectangle \(A B C D\)

In Exercises 23 to \(26,\) find an equation for each sphere. With center \((0,0,0)\) and containing the point \((3,12,-5)\)

Use the Distance Formula to show that the circle with center \((0,0)\) and radius length \(r\) has the equation \(x^{2}+y^{2}=r^{2}\)