# Questions and Answers

# Your Questions About X1

Helen asks…

## How to check if coordinates are parallel or perpendicular?

So Im in need of help! So my math calss got a class project which is due tomorrow…We had to graph something which I did and now we have to find the perpendicular lines and parallel. The thing I graphed isent a certain shape. I dont know how to find the perpendicular and parallel lines, I tryed the y2-y1 x2-**x1** thing but the answers werent right…Can someone help?

### Administrator answers:

Basically you just need to use the definition. Parallel lines have the identical slope, while perpendicular lines will have opposite the inverse of the slope (i.e. Slope is m, then the perpendicular line has slope of -1/m).

It’s difficult to go further than that without knowing specifics of what you’re dealing with.

Laura asks…

## What are two ways to find average velocity?

It should be more or less simple its only the first week of physics. One is average velocity= distance traveled/ time

The other has this format maybe?: average velocity= (**x1**-x2)/2

errrr, you repeated the first one i said more or less, wats another way to find average velocity?

### Administrator answers:

Average velocity is given by the change in position divided by the change in time over a distance or time interval.

Time Interval (t1, t2)

Resulting Position Interval (d1, d2)

Average Velocity, Va = (d2 – d1) / (t2 – t1)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Michael asks…

## What is the equation for the area of a quadrilateral using vertices?

I have seen two different equations on this problem, and each claimed the other was wrong?

Use the vertices, (1,1), (-2,6), (3,6), (5,4), if you want.

Or,

**X1**=1, Y1=1

X2=-2, Y2=6

X3=3, Y3=6

X4=5, Y4=4

Thanks in advance, Happy Thanksgiving to all.

### Administrator answers:

The reason why you found two answers is because with the 4 vertices you defined 3 different quadrilateral, one that is simple and convex (rhomboid to be precise), and two complex ones.

If the vertices are labeled A,B,C and D you get the next quadrilaterals:

ABCD, ACBD, ACDB.

The area of the simple is equal to the sum of the area of the 2 complex ones.

P(ABCD)=P(ACBD)+P(ACDB)

Hence each equation claimed the other was wrong. In fact there are three different answers to the question.

Solving the example is left for you. Probably you have solved it right two times.

Chris asks…

## What is the formula to find out average percent increase in a price of a house?

Lets say a house sold for $200,000 today and was purchased for $100,00 five years ago. Of course, it did not increase 20% annually (100,000 x 1.2 **x1**.2 **x1**.2 **x1**.2 **x1**.2) so how so I figure out average increase?

### Administrator answers:

The prior answer is exactly right, but as far as a general rule goes:

Divide the current value by the present value – here, $200,000 divided by $100,000 = 2

If you want to figure out the average increase over x periods, simply take the xth root of the quotient you calculated above.

Here, again, for example, you’re looking for the 5th root of 2, because you’re trying to figure out the average increase over 5 years (therefore, the 5th root) of 2 (the quotient)

So – using that formula here:

The 5th root of 2 (the same as 2 raised to the 0.2 power) equals 1.14869.

Ignore the leading 1 – you’re looking for the numbers after the decimal place. Therefore, the average rate of growth is 14.869 percent per year over 5 years.

This approach should work for any similar problem.

Good luck!

Mark asks…

## What is the formula to find out average percent increase in a price of a house?

Lets say a house sold for $200,000 today and was purchased for $100,00 five years ago. Of course, it did not increase 20% annually (100,000 x 1.2 **x1**.2 **x1**.2 **x1**.2 **x1**.2) so how so I figure out average increase?

### Administrator answers:

(future value/present value)^(1/time)

So using your example, (200,000/$100,000)^(1/5) or the fifth root of 2, which is 1.148698 or 14.8698%.

To use your example, 1.148698 x 1.148698 x 1.148698 x 1.148698 x 1.148698 =2

Just be careful with your units of time. If you had found the monthly rate, you could not multiply it by twelve to find the annual rate, you would take it to the twelth power.

One simpler method, that is approximately correct is the rule of 72. You can estimate most rates by dividing 72/time. In this case it would give you 14.4. It comes in handy when you don’t have a calculator on hand. See the wikipedia article on why it works.

Carol asks…

## What is the formula to find out average percent increase in a price of a house?

Lets say a house sold for $200,000 today and was purchased for $100,00 five years ago. Of course, it did not increase 20% annually (100,000 x 1.2 **x1**.2 **x1**.2 **x1**.2 **x1**.2) so how so I figure out average increase?

### Administrator answers:

If a = average annual increase,

200000 = 100000 times (1+a)^5

2 = (1+a)^5

so 1+a = fifth root of 2 = 2^(1/5) or about 1.1487. So a = about .1487 or 14.87%

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