Anyone knows anything about slopes?

Question

Yes, slopes are easy, but with the problems my teacher is giving me- it seems to be hard. This is the question-
1) The coordinates for a quadrilateral are A (12,4), B, (8,12), C (-8,4), and D (-4, -4). What is the best description for the shape?

Choices: A-square B-Rectangle C-Rhombus D. General Quadrilateral

I did the problem and I got a AB-4 BC-17.9 CD-8.9 DA-17.9 If that is right, what shape should I pick If I only have two sides congruent and the other two not congruent and totally opposite. Did I do the problem right in the first place?

Answer 1

If you are allowed, plot it first so you can have a picture of how it looks like before calculating..so here it goes,

Sorry but I think you miscalculated the slopes.

Slope AB = (Yb - Ya) / (Xb - Xa)
= (12 - 4) / (8 -12) = 8 / -4
= -2

Slope BC = (Yc - Yb) / (Xc - Xb)
= (4 - 12) / (-8 - 8) = -8/-16
= 1/2

Slope CD = (Yd - Yc) / (Xd - Xc)
= (-4 - 4) / (-4 - -8) = -8 / (-4 + 8)
= -8 / 4
= - 2

Slope DA = (Ya - Yd) / (Xa - Xd)
= (4 - -4) / (12 - -4) = (4 + 4) / (12 + 4)
= 8/ 16
= 1/2

From the values of the slopes you can tell whether the
lines are parallel or perpendicular (at right angles).

*a line is perpendicular to another if it's slope is a negative reciprocal of the other
*parallel lines have equal slopes

Here are the values of the slopes,

Slope AB = -2
Slope BC = 1/2
Slope CD = -2
Slope DA = 1/2

Therefore,
AB is parallel to CD and both perpendicular to BC and DA.
BC and DA are also parallel to each other.

Meaning,
1. AB and BC are at right angles.
2. AB and DA are at right angles.
3. CD and BC are at right angles.
4. CD and DA are at right angles.
5. AB = CD
6. CD = DA.

Now you are only left with two choices the SQUARE and RECTANGLE.

To find out, you can calculate AB or CD and BC or DA
to check if the 4 sides are of the same length or not.

Using pythagorean theorem to get distance between two points,

AB = square root of [ (Xa - Xb) ^2 + (Ya - Yb) ^ 2]
= sq rt of [ (12-8)^2 + (4-12)^2 ]
=sq rt of [ 4^2 + (-8)^2]
= sq rt of [ 16 + 64]
= sq rt of 80

BC = sq rt of [ (Xb - Xc)^2 + (Yb - Yc)^2]
= sq rt of [ (8 - -8)^2 + (12 - 4)^2]
= sq rt of [ 16^2 + 8^2]
= sq rt of [ 256 + 64 ]
= sq rt of 320



Therefore, it is a RECTANGLE since not all sides are of the
same length.

Answer 2

Well... you could just plot them and draw them out to see the shape, but the slopes you got are the "lengths". And the length I found for
AB is 8.9.
So I saw a rectangle... also if you did the slopes for all of them you would see that
CB and DA are parrallel
so the length AB and CD have to be the same.

Answer 3

First thing is to draw it on graph paper and see what it looks like. Then you can start proving it to be what you think it is.

Calculate the lengths of all the sides. Then calculate the length of one of the diagonals. That's all you need. You don't need to look at slopes at all, because if the angle is a right angle, then the diagonal squared is the sum of the squares of the two sides.

Answer 4

Given those slopes, you have two parallel sides, and two non-parallel sides. You have a "trapezoid." If those four are you only choices, then I suppose you have to chose "D. General Quadrilateral." All three of the other shapes are defined to have opposite sides that are parallel.

Answer 5

The easiest way to find out is to plot the points on graph paper.

Slope between two points = (y2 - y1) / (x2 - x1) Recheck your slopes, and be careful when subtracting negative numbers from other negative numbers, etc.

Answer 6

nonetheless, i think of agencies might like cyborg workers, meaning opposing gay marriage is comparable to opposing our wonderful activity creators. in case you oppose gay marriage, you're a socialist who's attempting to get in the way of earnings. actuality.