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## High school geometry

### Course: High school geometry>Unit 6

Lesson 3: Problem solving with distance on the coordinate plane

# Coordinate plane word problem

Watch Sal solve an example where has to determine which of the Minions a wizard can reach using the coordinate plane. Created by Sal Khan.

## Want to join the conversation?

• why is it 3 square roots of 2 instead of the square root for 18?
• Sal was just re-writing it in a way that makes it a little more obvious what the decimal value of the number would be. `3√2` is clearly greater than `3` but less than `6`. However, for the purpose of the original question (as you can see near the end of the video) it's actually easier to leave the result as `√18` - that makes it easier to compare to the `√36` spell length and to the other minion distances.
• Why does Sal put Absolute Value signs around the change in x and y? Isn't distance always positive? (Around -)
• Distance is always positive but change in x's and y's can be negative.
E.g. change in x's between A(4;9) and B(1;9) is equal to 1-4=-3, but distance is 3 ( |-3|=3).
• how is sqrt(9 +9) = 3sqrt(2)?
• Use the fact that 9+9 = 2*9
Sqrt(9+9) = sqrt(2*9) = sqrt(2) * sqrt(9) = 3*sqrt(2) , and this is the most you can simplify the radical because 2 has no repeated factors except for 1.
• At what is the little number going down?
• Subscript to indicate that which point it belongs to. In the example we had 2 points with the (x,y) coordinates. If we labelled them both (x,y) it will be confusing. So we assign either point to be point 1 (usually the first given point) and the other is point 2. So point 1 has the coordinate (x subscript 1, y subscript 1) and point 1 has the coordinate (x subscript 2, y subscript 2)
• Why doesn't he just use the distance formula?
• The distance formula is basically the same thing as the Pythagorean Theorem so he can use the distance formula or the Pythagorean Theorem. It doesn't matter at all. Also, as you may have noticed, Sal isn't very fond of memorizing formulas :)

However, he basically DOES basically use the distance formula.
• if (b,b-1),(b+2,b+1) and (b,b+3) are three consecutive points of a square what's its area?
• Since we know it is a square, we only need to know the length or distance of one side to find the area. To find the distance we use Pythagorean theorem , or d=√((change in x)²+(change in y)²) or d=√((y₂-y₁)²+(x₂-x₁)²)

Point 1 (x₁,y₁) given (b, b-1) and point 2 (x₂,y₂) given (b+2,b+1)
We can identify x₁=b and x₂=b+2, therefore (x₂-x₁)²=(b+2-b)²=2²=4
And y₁=b-1, y₂=b+1, so (y₂-y₁)²=((b+1)-(b-1))²=(b+1-b+1)²=2²=4

So d=√((y₂-y₁)²+(x₂-x₁)²)=√(4+4)=√8
Area of the square is A=S²=(√8)²=8 (unit)²
• At , what does the triangle thing represent?
(1 vote)
• The triangle thing is the greek letter "delta", and it can be used to denote "change in" when you're doing math or science.
• I know this is a bit off topic but what grade would you learn to find the area of a triangle with given vertices.
• Area of the triangle with angles at the vertices? I'm not sure what you're talking about.
I'll assume you're talking about geometry which is a 10th grade subject, to trig which is taken after algebra 2.