Exam 11: Analytic Geometry

The fourth vertex of the parallelogram shown is ( ).

If the diagonals of a parallelogram are congruent, then the parallelogram isa rhombus.

Given that A = (-3,-7)and B = (5,2), find the midpoint of .

Where ,find the slope m of the line that contains the points ( a ,3)and ( b ,3).

Determine the value of  a so that the point lies on the plane .

Find the area of , which has vertices at (0,0), (8,0), and (5,6).

Where A = (4,-7)and M = (3,-2), point M is the midpoint of . Find the coordinates for point B .

In the form , find the equation of the line that contains ( g , h )and is perpendicular to .

Find the midpoint of the line segment that joins (2a,0)and (0,2b).

For any point  in Cartesian space, explain why the point  is the point of symmetry with respect to the origin.

Explain why the plane  is a plane of symmetry for the sphere  .

Find the area of , which has vertices at A (-2,-3), B (-2,4)and C (5,4).

The midpoint of the line segment that joins the point (0,0,0)to the point (2,-2,2)is the point (1,-1,1).

Where , the slope of the line through the points ( )and ( )is .

The drawing shown can be used to prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side.

Find a direction vector for the line that contains the points and .

Determine the value of x so that the points (-2,4), (1,1), and (x,6)are collinear.

The line shown has a positive slope.

Find the distance between the points (-7,-5)and (5,4).

Find the distance between the points (3,-4)and (-2,8).