Exam 11: Analytic Geometry

Which equation must hold true if the parallelogram shown is a rhombus?

Find the distance between the points (-4,3)and (5,3).

For square ABCD, two of the vertices are A = (0,0)and B = (a,0). Provide coordinatesfor the remaining vertices.

Find the distance between the points and .

For the isosceles triangle shown, the coordinates of the vertex have not been provided.In order, use a, b, c, etc as needed to name the coordinates of the vertex.

Find the Slope-Intercept form of the equation whose graph has slope m = 2 and the y-intercept at (0,-3).

(not shown)has vertices A (0,0), B (2 a ,2 b ), and C (0,2 c ). Where M is the midpoint of and N is the midpoint of , how are the lengths of and related?

The graphs of the equations and are the same line.

The lines which are the graphs of and intersect at one point.

Explain why the lines decribed below are parallel.          and

For the isosceles triangle shown, which of the following must be true?

For the parallelogram ABCD with vertices A (0, 0), B ( a , 0), C ( ), and D ( b , c )to be a rhombus, it is necessary that .

Find the midpoint of the line segment that joins (-1,4)and (7,-8).

Lying on the x-axis are 2 points whose distance from (2,-3)is 5 units. Find the x-coordinatesof these points (a,0)that lie on the x-axis.

Where a, b, c, d, . . . , and n are real numbers, explain why the line          has the direction vector .

Find the point that is the y -intercept of the line .

What is the slope of any line that is perpendicular to the graph of ?

Find the slope of a line that is perpendicular to the line through the points ( a , b ) and ( ).

Find the area of the triangle with vertices at (2a,0), (2c,0), and (0,2b).

The line with equation y = mx + b has slope m and contains the point (0, b).