Math test #3

Question 1

Midpoint formula

Answer 1

(x1+x2)/2, (y1+y2)/2

Question 2

What can midpoint be used for

Answer 2

to find middle of line, for the perpendicular bisector, and to find an unknown point

Question 3

Distance formula

Answer 3

square root of (x2-x1)2 + (y2-y1) 2

Question 4

slope inercept form

Answer 4

y =mx + b
m is gradient
b is y intercpt

Question 5

how to find gradient

Answer 5

(y2-y1)/(x2-x)

Question 6

gradient in word problems

Answer 6

distance/time
amount of money/time
rise/run
rate of change in y with respect to change in x

Question 7

Standard form

Answer 7

ax+by=c

Question 8

how to graph standard form

Answer 8

either turn into slope intercept form (if numbers aren’t nice, you can put any number as x and solve for y to find good points)
or
find intercepts by making x=0 and solving for y
then y=0 and solving for x

Question 9

how to graph slope intercept form

Answer 9

m = gradient
b = y intercept
go to y intercept and count for the gradient

Question 10

how do you verify if a point is on the line

Answer 10

insert point into slope intercept form and if its true, it is. if its false, it isnt

Question 11

Inequalities

Answer 11

same as equations but with inequality instead
graph the same as an equation but shade one region based on if the line works with point (0,0) or (1,1)

Question 12

What are simultaneous equations used for

Answer 12

to find intersection point of two lines (perpendicular bisector)

Question 13

how to solve simultaneous equations graphically

Answer 13

plot both lines and determine where they intersect based on graph

Question 14

how to solve simultaneous equations with substitution

Answer 14

y=2x+3
y=3x+2
take away Ys and put the two equations into one (with only x as variable). Solve for x then plug answer into original equation to find y

Question 15

How to solve simultaneous equations with elimination

Answer 15

place two equations on top of each other so that the negative and positive versions of the same number are together. Have them cancel out and then solve for the other variable. Plug the answer into one of the equations
3x+2y=5
x-2y=3
4x=8
x=2
if the numbers aren’t nice, then multiply until they are

Question 16

Parallel lines

Answer 16

same gradient different y intercept

Question 17

perpendicular lines

Answer 17

negative reciprocal of gradient and different y intercept

Question 18

how to find perpendicular bisector

Answer 18

• find slope of line, midpoint, and y intercept
• do negative reciprocal of slope for perpendicular line
• put midpoint into x and y coordinates to find b intercept (of the perpendicular line)
• Use simultaneous equations to solve for intersection

Question 19

How to find shortest distance from point to line

Answer 19

Perpendicular bisector
then use distance formula from intersection point and point given

Question 20

what is the equation of a circle

Answer 20

r2 = (x-h)2 + (y-k)2
r = radius
and center of circle = (h,k)