Answer:
<em>not</em> a rectangle
Step-by-step explanation:
There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.
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The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.
... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2
The slope of AD is computed in similar fashion.
... AD slope = (-2-5)/(-2-(-5)) = -7/3
The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.
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Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC <em>is perpendicular</em> to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.
For 3x + 5:
5 is the y-intercept and 3(also 3/1) is the rise over run
Answer:
(6,20) because both lines pass through this point
Step-by-step explanation:
To solve this you can use the substitution method.
Since both of them are equal to y, substitute one of the equations for y, that way you have x+14 = 3x+2. From here you continue to simplify.
Eliminate x from either side of the equation. For example, subtract x from the side that says "x+14". (Make sure you are also subtracting it from the other side of the equal sign as well.
Once you do this you should now have 14 = 2x+2
In order continue, you now have to get x by itself. So now subtract 2 from both sides of the equation. After doing this, you should have 12 = 2x
You then simplify x by dividing both sides by 2. This will get you x = 6
Now that you have the x-value, substitute that into either of the two equations (it is recommended you substitute it into both equations to make sure you have the correct x-value). For example: If I substitute x into Line C's equation, I will now have y = 6 + 14.
6 + 14 is 20, therefore you're y-value is y = 20
Answer:
17 1/3
Step-by-step explanation:
the correct answer is 17 1/3