ACT Coordinate Geometry Identifiers

2014

COORDINATE GEOMETRY
IDENTIFIERS

Presented By TutorByDenise
www.tutorbydenise.com
1/1/2014

COORDINATE GEOMETRY IDENTIFIERS

When ask you for slope, equation should look like y=mx +b but will not
For example find slope 2y + 4x = 8
REMEMBER the number next to the “x” will be the slope ONLY IF equation is in the y= mx + b format
Our equation has

• a “2” next to the “y”
• It has 4x (which is mx) on the left side instead of the right side
We have to fix those two items How?
1st : The only thing on the left side should be the y; to get rid of everything else do the opposite sign
• Our case has +4x so we subtract (-4x) on both sides of the equal sign
• 2y + 4x = 8

-4x = -4x
2y = -4x + 8
Now you should have y on the right side of the equation and mx and b on the left side
2nd: There should be no numbers next to the “y”, to get rid of a number next to y divide number
• In our case we are dividing 2 on both sides of the equal sign
• 2y = -4x + 8
2= 2 2
Y = 2x + 4
The slope is 2
Parallel slope is the same mx so slope would be 2
Perpendicular slope is opposite sign and flipped number so it would be -1/2

What do you do when they ask about the distance between or how far apart are..?

Check out the next page

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COORDINATE GEOMETRY IDENTIFIERS

When they ask you distance of… you will need to use pythagoreon theory
(sort of)
Know formula a2 + b2 = c2 (I know you knew that)
In this case use the the x’s as the a’s and the y’s as the b’s and your
distance is c2.
For an example find the distance between (8,-2) and (-1,3)
Our x are 8 and -1 and our y are -2 and 3
We subtract not add the x’s and do the same with our y’s
Step 1: so insert your x’s into the parenthesis (8 – (-1))
Step 2: insert your y’s into the parenthesis (-2 – (-3)
Step 3: insert back into equation a2 + b2 = c2…….. (8 – (-1))2 + (-2 – (-3)2 =
c2
Step 4: Calculate 92 + -52 = c2
106 = c2
But we want Distance not distance2. How do we find that?
By taking the square root
Step 5: √106 can not be simplified so this is our answer

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COORDINATE GEOMETRY IDENTIFIERS

Well if they ask you to find the Midpoint you know that’s just the middle of
the points

You’re a genius!
So how do you do that?
Each endpoint has an x coordinate and a y coordinate right? (of course)
So we add both of the x coordinates and divide by 2 and we’ll get the
middle x point and we do the same for the y coordinates
Here’s an example. Find the midpoint of (6,9) and (10,1)
Our x are 6 and 10 (the 1st number in the grouping…x comes before y )
Our y are 9 and 1 (the 2nd number in the grouping)
Step 1: add both x our case 6 + 10 = 16
Step 2: divide by 2 16/2 = 8
Step 3: add both y our case 9 + 1 = 10
Step 4: divide by 2 10/2 = 5
Step 6: midpoint (8,5)

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