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zavuch27 [327]
3 years ago
12

The coordinates of the vertices of ANGLE RST are R(-3,5), and S(4,5), and T(4,-2). Find the side lengths to the nearest hundredt

h and the angle measures to the nearest degree.
Mathematics
1 answer:
e-lub [12.9K]3 years ago
6 0


Side lengths: RS=7 and ST=7, and angle=90 degrees

Why?

Since second coordinates of R and S are the same so we can just count the length by adding first coordinate of R and first coordinate of S= |-3|+4=7

Since first coordinates of R is the same as first coordinate of T so we can just count  the length  by adding second coordinates of S and T=5+|-2|=7

Angle: RST is =90 degrees because triangle RST is right angled  triangle. Why? Because RS is parallel to X axis(the same second coordinates of R and S) and ST is parallel to Y axis(the same coordinates of S and T) .


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alekssr [168]

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First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m=

0 - 2

4 - 0

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m=

-2

4

or...

m=-1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(4,0). When x of the line is 4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-1/2x+b. b is what we want, the -1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=-1/2 × 0+b, or solving for b: b=2-(-1/2)(0). b=2.

(4,0). y=mx+b or 0=-1/2 × 4+b, or solving for b: b=0-(-1/2)(4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (4,0)

is

y=-1/2x+2

4 0
3 years ago
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