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3 years ago

PLEASE HELP. IF U GET THIS RIGHT I WILL MARK U BRAINLIEST!!! THANK U GUYS

Mathematics

1 answer:

KatRina [158]3 years ago

6 0

Answer:

Step-by-step explanation:

The slope is the rise over the run. 2 simple coordinates I can see is (6,2) and (7,4). I usually like to visualize it instead of actually solving it mathematically. So, we can start at (6,2). The point (6,2) goes up 2 and 1 to the right in order to get (7,4.) So since the slope is rise over run ( y/x) it would be 2/1 because we went 2 up the y axis and 1 to the right of the x axis. So 2/1 is 2. Therefore, 2 is the answer. I'm sorry if my explaining isn't the best... I hope this helps though!!

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The vertices of a square CDEF are C(1,1), D(3,1), E(3,-1) and F(1,-1). What formulas prove that the diagonals are congruent perp

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To prove that the diagonals are congruent, you need to formula to compute the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$

Using that formula, you may prove that $d(C,E) = d(D,F)$ , which means that the two diagonals have the same length.

To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by

$m = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

You can use this formula to prove that

$m_{CE} = -\cfrac{1}{m_{DF}}$

In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.

Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is

$y-y_0 = m(x-x_0)$

where $(x_0,y_0)$ is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:

$\begin{cases} y= m_{CE}x+q_{CE}\\ y = m_{DF}x+q_{DF} \end{cases}$

And use again the formula for the distance between two points to prove that

$d(A,C) = d(A,D) = d(A,E) = d(A,F)$

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3 years ago