IMC-Unit 1 Study Guide
Distance
√(
)
(
)
Midpoint
(
)
Slope
m=
Negative
Slope
m=
Vertical
m = und
Positive
m=
Positive slope-increases from L R
Negative slope-decreases from L R
Horizontal
m=0
Horizontal Line-Slope = 0 (This would result from a numerator of 0)
Vertical Line-Slope is undefined (This would result from a denominator of 0)
lines have opposite reciprocal slopes (EX.
and
m = 0 and m = und
lines have the same slope (EX. m = and m = )
Solving for intercepts
x-intercept- set y = 0 and solve for the x-value should be written as (x, 0)
y-intercept- set x = 0 and solve for the y-value should be written as (0, y)
m = 1 and m = -1)
Parallelograms
Properties
1.
2.
3.
4.
5.
Opp sides
Opp sides
Opp ’s
Diagonals bisect each other
Consecutive <’s are supplementary
To show a quadrilateral is a parallelogram.
1. Use the midpoint formula to show the diagonals bisect each other, or have the same midpoint.
2. Use the distance formula to show BOTH pairs of opp sides are .
3. Use the slope formula to show the opp sides are , or have the same slope.
4. Use the slope and distance formula on ONE pair of opp sides to show it is BOTH and .
Writing Equations of lines
Goal-Solve for m and b to write the equation
Slope intercept form
y = mx + b
Standard form
Ax + By = C
m = slope
b = y-intercept (0, b)
1. A must be positive
2. A, B, and C must be whole numbers (no fractions)
3. Can also be Ax + By + C = 0
1. Given a point and a slope
-plug into y = mx + b and solve for b
-write the equation
2. Given two points on the line
-use the two points to find the slope
-plug either point and the slope into y = mx + b to solve for b
-write the equation of the line
3. Given an equation of a line and a point
-put the equation into slope-int form and identify the slope
-plug the same slope and the given point into y = mx + b to solve for b
-write the equation of the line
4. Given an equation of a line and a point
-put the equation into slope intercept form and identify the slope
-put the opposite reciprocal slope and the given point into y = mx + b to solve for b
-write the equation of the line using the opposite reciprocal slope and b
5. Writing the equation of a median to ̅̅̅̅ in triangle ABC
-the median comes from a vertex to the midpoint of the opposite side of the triangle
-find the midpoint of ̅̅̅̅
-use the vertex A and the midpoint of ̅̅̅̅ to find the slope of the median
-plug either point and the slope into y = mx + b to solve for b
-write the equation of the line
A
C
B
Mdpt of ̅̅̅̅
𝐵𝐶
6. Writing the equation of an altitude to ̅̅̅̅ in triangle ABC
-the altitude comes from a vertex to the opposite side of the triangle
-find the slope of ̅̅̅̅
A
-use the opposite reciprocal slope
-plug the slope and the vertex A into y = mx + b to solve for b
-write the equation of the line
B
7. Writing the equation of a bisector
-the bisector of a segment is perpendicular at the segment’s midpoint
-find the slope and midpoint using the given points or vertices
-plug the slope and midpoint into y = mx + b to solve for b
-write the equation of the line
Standard form
Ax + By = C
-multiply both sides of the equation by the least common multiple of the denominators
-move the terms to the appropriate sides of the equation
-divide each term by -1 if necessary to change the sign of A
C
Simplifying Radicals
Remember
-“outside with outside and under with under”
-“you need a buddy to leave the house”
√
√
=
√
6
8
3 2 4 2
3 2 2 2 2
√
16
4
√
√
6
4 2 3
2 2 2 2 2 3
√
√
√
√
9
3
3
10
5
2
√