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Aneli [31]
3 years ago
7

Point X has coordinates (-4, -5) and point y has coordinates (--1, --5 ) which expression models the distance between points X a

nd Y ?

Mathematics
1 answer:
sdas [7]3 years ago
4 0

Answer:  The last expression shows the result of 3  so it models the distance between x and y.

Step-by-step explanation:

First you will have to  find the distance between the two points by square the x coordinates and squaring the y coordinates to find their sum .  

-4 - (-1) = -3

-5 - ( -5) = 0

-3^2 + 0^2 = d^2   where d  is the distance

9  = d^2

d= 3  

The distance is 3 units  

Now evaluate which expression have a solution as 3.

The last expression is the answer

the absolute value for -4 is 4   , and the absolute value for -1 is 1  and 4 minus 1 is 3.

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<h3>Answer:  (4,2)</h3>

==============================================================

Explanation:

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Reflecting over y = 1 lands the point on (0,2) because we move 1 unit up to arrive at the line of reflection, and then we keep going one more unit (same direction) to complete the full reflection transformation. I'll call this point P.

Then we reflect point P over the line x = 2 to arrive at the location Q = (4,2). Note how we moved 2 units to the right to get to the line of reflection, and then keep moving the same direction 2 more units, then we have applied the operation of "reflect over the line x = 2"

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All of this is shown in the diagram below.

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<h3>                1)  x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2</h3><h3>                2)   x_1=-\dfrac13\,,\quad x_2=-3    </h3>

Step-by-step explanation:

<h3>1)</h3>

x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2

<h3>2)</h3><h3>3x^2 + 10x=-3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b =10\,,\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}= \dfrac{-10\pm\sqrt{100-36}}6\\\\x_1=\dfrac{-10+\sqrt{64}}6=\dfrac{-10+8}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}6=-3</h3>
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3 years ago
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