0 - Pre-Calculus 1 (Bridging)

Other term for Cartesian Plane

RCS (Rectangular Coordinate System)

Every point on the plane is identified as?

Ordered Pair (x,y)

What do you call the three coordinates?

X - Abscissa
Y - Ordinate
Z - Applicate

What are the signs per quadrant?

Just imagine the RCS

A point in geometry is a […}

Location

A point (x,2) is equidistant from the points (-2,9) and (4,-7). Then the value of x is […]

3.67

Find the distance between two points A(4,1,-5) and point B(-3,3,6) in a space.

13.19

The endpoints of a line segment are A(-6,8) and B(10,-4). Find the midpoint M of AB.

M = (2,2)

Describe a line

• straight

• no thickness (1D)

• extend both directions

• constant slope and inclination

Define slope

m = rise / run = (y2 - y1) / (x2 - x1)

Define angle of inclination

tanθ = m

Relationship of slope and angle of inclination

positive slope - 0 to 90
negative slope - 90 to 180

Determine the distance, slope, and angle of inclination of the line connecting point A(3,-5) and B(4,-1)

d = sqrt(17)
m = 4
θ = 75.96

Define point-slope form

y - y1 = m (x - x1)

Define two-point form

y - y1 = [ (y2 - y1) / (x2 - x1) ] (x - x1)

Define intercept form

x/a + y/b = 1

Define slope-intercept form

y = mx + b

Find the smaller angle between the lines 4x + y = 10 and -3x - 5y = 8

θ = 45 deg

Define the slopes of parallel and perpendicular lines

Parallel: m1 = m2
Perpendicular: m1 = -1 / m2

The general equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = -6 is:

3x - 2y -12 = 0

Find the equation of the line normal to line 2x + 8y - 7 = 0 which passes through the point P(-2,6)

4x - y + 14 = 0

Find the equation of the line parallel to 3x - 4y + 12 = 0 passing through P(2,-3)

3x - 4y - 18 = 0