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nikdorinn [45]
3 years ago
8

How do I find the orthocenter of the triangle with these coordinates(8,10)(5,-10)(0,0)

Mathematics
2 answers:
WINSTONCH [101]3 years ago
7 0
Find the equation of 2 of the line segment, then find the perpendicular lines to them, then solve for x by making the perpendicular equations equal

laila [671]3 years ago
5 0
A (0,0), B(8,10), C(5,-10)
First, find the slope of AB and AC, slope of AB is 5/4, slope of AC is -2
next, find the negative reciprocals of the slopes: -4/5 and 1/2 respectively
so the altitude of AB is a line with a slope of -4/5 passing through (5,-10)
the altitude of AC is a line with a slope of 1/2 passing through (8,10)
find these two lines:
Plug (5,-10) in y=(-4/5)x+b to find b, b=-6, so y=(-4/5)x -6
plug (8,10) in y=(1/2)x +b to find b, b=6, so y=(1/2) x +6

the point where these two lines meet is the orthocenter.
y=(-4/5)x -6
y=(1/2) x +6
(-4/5)x -6=(1/2) x +6
x=-120/13
y=(1/2)*(-120/13)+6=18/13
so the orthocenter is (-120/13, 18/13)
these numbers look odd, but I've run the vertex through an orthodox calculator, and got the same result.

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Answer: (\dfrac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .

Step-by-step explanation:

Transformation rule for dilation:

(x,y)\to(kx,ky) , where k = scale factor

Given : Scale factor = -\dfrac13

Parallelogram JKLM has vertices J(-1, 6), K(0, 9), L(6, −3), and M(3, −3)

Vertices after dilation:

(-1,6)\to(-1\times\dfrac{-1}{3},6\times\dfrac{-1}{3})=(\dfrac13,-2)

(0,9)\times(0\times-\dfrac13,9\times-\dfrac13)=(0,-3)

(6,-3)\to(6\times-\dfrac13,\ -3\times-\dfrac13)=(-2,1)

(3,-3)\to (3\times-\dfrac13,\ -3\times-\dfrac13)=(-1,1)

Hence, the coordinates of the image if the parallelogram = (\dfrac13,-2),\ (0,-3),\ (-2,1),\ (-1,1) .

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3 years ago
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The same story happens with the second equation. Plug in theta = 0 and it becomes

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Том и Эми установили будильники на своих телефонах на 6:45. Оба сигнала тревоги звучат одновременно в 6.45. Будильник Тома звучи
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Answer:

36 минут спустя в 7:21

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Итак, в 7:21, через 36 минут после того, как они ушли, и Том, и Эми проснулись, и они оба опоздали.

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Translation

36 minutes later at 7:21am

this is a LCM problem so this how to solve it.

Toms sounds at 9, 18, 27, 36 minutes after it initially sounds

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