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Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

The Cartesian Coordinate System and the Distance Formula

Hi, I need help finishing these up. I also need to make sure the ones I've done are correct.

1. Draw a Cartesian Coordinate system for yourself, and then determine whether these sets of points form triangles (C)

Set 1: (0,0), (1,1), (0,1)
Set 2: (-1, 0), (1,1), (3,2)
Set 3: (0,0), (5,0), (3,5)

Aset 1 line segment, set 2    Triangle, set 3 line segment
Bset 1 Triangle, set 2    Triangle, set 3 line segment
Cset 1 Triangle, set 2 line segment, set 3 Triangle
Dset 1 line segment, set 2 line segment, set 3    line segment
E set 1 Triangle, set 2    line segment, set 3 line segment
F set 1 line segment, set 2 Triangle, set 3 Triangle

2. I have placed a square that is 2 units long on each side so that its sides are parallel to
the x- or y-axis, but it's center is right on the origin. What are the coordinates of the corners? (B)

A (-1,-1), (1,-1), (-1,-1), (1,-1)
B(1,1), (1,-1), (-1,1), (-1,-1)
C(-1,-1), (-1,-1), (1,-1), (1,-1)
D(1,-1), (-1,1), (-1,-1), (-1,1)
E (-1,1), (-1,1), (-1,-1), (-1,-1)
F (1,1), (1,1), (1,1), (1,1)

3. What shape do these four points make? (Draw from one to the next in the order given,
and then draw from the last back to the first).

(0,-1), (1,1), (0,3), (-1,1)  (E)

AA pentagon
BAn octagon
C A triangle
DA square
E A rhombus
F A cube

4. Now do the same with this list, and describe the shape. (B)

(0,-1), (0,3), (1,1), (-1,1)

AA square
BTwo acute angles that meet at the acute angles
CA triangle
DTwo right triangles that meet at the right angles
E A rhombus
F Two obtuse triangles that meet at the hypotenuse

What shape is created by the following points? (Do not connect these in order, just connect around the outside of the shape.)

5. (-1, 0), (2, 0), (2, 4), and (-1, 4) (A)

Aa rectangle
Ba square
Ca parallelogram
Da rhombus
E a triangle
F a line segment

6. (-2, 1), (-6, 1), (-7, 6), and (-3, 6) (F)

Aa line segment
Ba trapezoid
Ca square
Da rhombus
E a triangle
F a parallelogram

7. (1, 1), (1, -3), (9, 1), and (5, -3) (A)

Aa line segment
Ba trapezoid
Ca square
Da rhombus
E a triangle
F a parallelogram

8. (8, 5), (2, -3), (5, -3), and (5, 5) (B)

Aa parallelogram
Ba trapezoid
Ca square
Da rhombus
E a triangle
F a rectangle

9. (-5, 1), (2, 1), (2, -4), and (-13, -4) (A)

Aa trapezoid
Ba line segment
Ca square
Da rhombus
E a triangle
F a parallelogram

10. (-7, 9), (-3, 13), and (-11, 13) (D)

Aa rhombus
Ba trapezoid
Ca square
Da right triangle
E a circle
F a line segment

Find the distance between the two points:

11. (-20, -4) and (-7, -6)

A4
BSQRT(61)
CSQRT(290)
D5
E SQRT(173)
F SQRT(180)

12. (1, 1) and (-4, 1) (D)

A4
BSQRT(61)
CSQRT(290)
D5
E SQRT(173)
F SQRT(180)

13. (-3, 22) and (-14, 35)

A4
BSQRT(61)
CSQRT(290)
D5
E SQRT(173)
F SQRT(180)

14. (9, -0) and (-3, -8)

A4
BSQRT(61)
CSQRT(290)
D4[SQRT(13)]
E 5[SQRT(17)]
F 3[SQRT(180)]

15. (1, 2) and (5, 2) (E)

A4[SQRT(13)]
BSQRT(61)
CSQRT(29)
DSQRT(202)
E 4
F SQRT(60)

What is the radius of a circle with the given center C that passes through the given point Z?

16. C (0, 0); Z (-8, 0)

A4
BSQRT(61)
C8
D5
E SQRT(173)
F SQRT(180)

17. C (-4, -5); Z (-10, -5)

A4
BSQRT(202)
CSQRT(290)
DSQRT(61)
E SQRT(173)
F 6

18. C (-5, 8); Z (-5, 4)

A4
BSQRT(61)
CSQRT(290)
DSQRT(202)
E SQRT(173)
F 6

19. C (-5, 9); Z (6, 0)

A4
BSQRT(61)
CSQRT(290)
DSQRT(202)
E SQRT(173)
F SQRT(180)

20. C (-7, 6); Z (-13, -6)

A4
BSQRT(202)
CSQRT(290)
DSQRT(61)
E SQRT(173)
F SQRT(180)

I'm mostly concerned about 11-20. I put the answers I knew in parenthesis next to the question. ex. (E)

I got completely confused once it hit question 11.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

Hi;

11) E

12) D

13) C

What did you get for 14? Did you use the distance formula?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

I tried to do 14, but the answer I came out with wasn't on there. Could you walk me through it?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

First, do you know the distance formula?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

I think so

Its when you take two points and subtract the x values and the y values then you use the Pythagorean Theorem  (c^2 = a^2 + b^2) to find the third side (hypotenuse)?

so d = √(x2 - x1)^2 + (y2 - y1)^2

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

14 has these two points.

(9, -0) and (-3, -8)

now which are x1 and x2?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

-3 is x2, 9 is x1

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

That is correct and y1 and y2?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

-8 is y2 and -0 is y1

d = √(-3 - 9)^2 + (-8 + 0)^2

Right?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

Yes, that is correct but you can drop the -0 from now on. 0 is just plain 0.

What did you get in the first bracket?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

(-12)^2

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

That is correct , now what does that equal?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

144

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

That is correct! Very good.

What is the next bracket?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

(-8)^2

So that would be 64

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

That is correct!

Now add them up.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

144 + 64 = 208

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

That is correct. What do you do now?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

now you do
√208

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

What did you get?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

14.4222051019

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

Does that match any of the answers?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

Nope, that's the answer I had originally.

The answers for that particular question are:
A: 4
B: sqrt(61)
C: sqrt(290)
D: 4[sqrt(13)]
E: 5[sqrt(17)]
F: 3[sqrt(180)]

Last edited by Nickiekinz (2015-04-02 04:45:52)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Cartesian Coordinate System and the Distance Formula

Did you know how to get D?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Nickiekinz

Member

Registered: 2015-04-02

Posts: 31

Re: The Cartesian Coordinate System and the Distance Formula

No clue