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Coordinate Geometry

Notes

Full Set

Coordinate Plane Formulas

1. Calculate the length, slope and mid-point of the line segments.

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2. Calculate the equation of each line.

standard form is y = mx + b

a) y intercept -2 and slope 3/4

b) through (-2 , 4) having a slope of -2/5

c) x intercept of -3 having a slope of 3/7

d) through the points (4,-1) and (-2,6)

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3. Complete the square and find the vertex.

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To 1 decimal place, find the coordinates of the point(s) of intersection of the graphs of

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The Equation of the Circle

a) what point is the center of the circle? _________________

b) what is the radius of the circle? ____________________

c) use the distance formula to find the equation of the circle.

a) what point is the center of the circle? _________________

b) what is the radius of the circle? ____________________

c) use the distance formula to find the equation of the circle.

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State the center and radius of each circle.

Graph the circle whose equation is

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Circle the point that is located on the circle

(3,-2) (-5,3) (5,-2) (0,3)

a) Find the x intercepts of the circle

Given the equation of a circle:

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b) find the y intercepts

Sketch the graph and find the domain and range.

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Circles and Completing the Square

standard form

general form

Put the equation of the circle in general form:

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Write these circles in standard form by completing the squares in both x and y. Give the center, radius, domain and range.

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Sketch this circle.

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Equation of the Tangent Line to a Circle

1. Give the equation of the circle. Then find the equations of the vertical and horizontal tangent lines to the cirle graphed below.

2. Find the equations of the horizontal and vertical tangents to the circle given by

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For all "slanted" tangents follow these steps:• sketch• find slope of radius• find slope of tangent line• use y = mx + b to find the equation of the tangent line

3. Find the equation of the tangent to at (4,-5).

For all "slanted" tangents follow these steps:• sketch• find slope of radius• find slope of tangent line• use y = mx + b to find the equation of the tangent line

4. Find the equation of the tangent to at (2,-1).

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Finding the Intersection Point(s) of a Line and a Circle

This will be a system of equations: use the method of substitution.

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Splitting a Segment into Equal Smaller Segments

Find the points that split (-10,5) to (6,1) into four equal smaller segments.

Split (-11,-6) to (9,9) into five smaller segments.

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Calculating the Distance between Points and Lines

1. Calculate the shortest distance between the point and each of the lines pictured in the following graph.

2. Calculate the shortest distance between the point and the line. The steps.• find the slope of the line• find the slope of the perpendicular line through the point• find the equation of the perpendicular line• solve the system to get the closest point• find the distance

The line y = -2x + 3 and the point (-5,1).

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3. Calculate the shortest distance between the point and the line. The steps.• find the slope of the line• find the slope of the perpendicular line through the point• find the equation of the perpendicular line• solve the system to get the closest point• find the distance

The line 2x + 3y - 6 = 0 and the point (5,4).

The Distance between Parallel Lines

1. Find the distance between the two horizontal lines.

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2. Find the distance between the two vertical lines.

3. Find the horizontal distance, the vertical distance and the shortest distance between the two parallel lines. y = 2x - 6 and y = 2x + 4

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4. Find the horizontal distance, the vertical distance and the shortest distance between the two parallel lines. 2x + 3y -6 = 0 and 2x + 3y + 12 = 0.

Verifying Conjectures

Consider triangle A(-1,3), B(1,7) andC(5,5).

a) verify that triangle ABC is a right triangle

b) M is to be the midpoint of AB and N the midpoint of AC. Verify that MN is parallel to BC.

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A line segment has endpoints M(8,6) and N(-6,8).a) verify that the endpoints are on the circle.

b) determine the equation of the line through the center of the circle and the midpoint of the chord MN

c) verify that the new line and MN are perpendicular

Proving Conjectures

Prove that the diagonals of a square are perpendicular.

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Coordinate Geometry - unit review

Calculate the length, the slope and the midpoint of the segment below.

Separate the segment from (-8,6) to (22,-6) into six smaller segments of equal length.

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• center• radius• domain• range• x intercepts• vertical tangents

Find

Calculate the equation of the tangent to

at (4,-1) .

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Find the shortest distance from the point (1,3) to the line 4x - 3y - 12 = 0.

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