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KengaRu [80]
3 years ago
7

BEING TIMED

Mathematics
2 answers:
irinina [24]3 years ago
7 0

Answer:

Therefore orthocentre is <em>( 5 , 1.5 )</em>

Step-by-step explanation:

From the general equation of a circle,

{x}^{2}  +  {y}^{2}  + 2gx + 2fy + c = 0

Substitute K(2, -2), L(4,6), M(8,-2) in (x,y)

K(2, -2): 2^2 +(-2)^2 + 2g(2) + 2f(-2) + c = 0

4g - 4f + c = -8

<em>Divide</em><em> </em><em>by</em><em> </em><em>4</em><em>:</em><em> </em><em> </em> g - f + c = -2 -----------<em>(</em><em>1</em><em>)</em>

<em>L(4,6)</em><em>:</em><em> </em>4^2 + 6^2 + 2g(4) + 2f(6) + c = 0

8g + 12f + c = -52

<em>D</em><em>i</em><em>v</em><em>i</em><em>d</em><em>e</em><em> </em><em>b</em><em>y</em><em> </em><em>4</em><em>:</em><em> </em> 2g + 3f + c = -13 ----------<em>(</em><em>2</em><em>)</em>

<em>M(8,-2)</em><em>:</em><em> </em>8^2 +(-2)^2 + 2g(8) + 2f(-2) + c = 0

16g - 4f + c = -68

<em>D</em><em>i</em><em>v</em><em>i</em><em>d</em><em>e</em><em> </em><em>b</em><em>y</em><em> </em><em>4</em><em>:</em><em> </em> 4g - f + c = -17 ----------<em>(</em><em>3</em><em>)</em>

<em> </em><em> </em><em><u>E</u></em><em><u>q</u></em><em><u>u</u></em><em><u>a</u></em><em><u>t</u></em><em><u>i</u></em><em><u>o</u></em><em><u>n</u></em><em><u> </u></em><em><u>(</u></em><em><u>2</u></em><em><u>)</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>(</u></em><em><u>1</u></em><em><u>)</u></em>

g + 4f = -11

g = -11 - 4f -----------(a)

<em><u>E</u></em><em><u>q</u></em><em><u>u</u></em><em><u>a</u></em><em><u>t</u></em><em><u>i</u></em><em><u>o</u></em><em><u>n</u></em><em><u> </u></em><em><u>(</u></em><em><u>3</u></em><em><u>)</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>(</u></em><em><u>2</u></em><em><u>)</u></em>

2g - 4f = -4

2g = -4 + 4f ----------(b)

<em>S</em><em>u</em><em>b</em><em>s</em><em>t</em><em>i</em><em>t</em><em>u</em><em>t</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em> </em><em>g</em><em> </em><em>i</em><em>n</em><em> </em><em>e</em><em>q</em><em>n</em><em> </em><em>(</em><em>b</em><em>)</em>

2(-11 - 4f) = -4 + 4f

-12f = 18

<em><u> f = </u></em><em><u>-</u></em><em><u>1.5</u></em>

<em><u>From</u></em><em><u> </u></em><em><u>eqn</u></em><em><u> </u></em><em><u>(</u></em><em><u>a</u></em><em><u>)</u></em>

g = -11 - 4(-1.5)

<em><u>g = -5</u></em>

<em><u>Since</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>orthocentre</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>given</u></em><em><u> </u></em><em><u>by</u></em><em><u> </u></em><em><u>(</u></em><em><u>-</u></em><em><u>g</u></em><em><u>,</u></em><em><u>-</u></em><em><u>f</u></em><em><u>)</u></em>

<em> </em><em> </em><em>There</em><em>f</em><em>o</em><em>r</em><em>e</em><em> </em><em>orthocentre</em><em> </em><em>is</em><em> </em><em><u>(</u></em><em><u>5</u></em><em><u>,</u></em><em><u>1</u></em><em><u>.</u></em><em><u>5</u></em><em><u>)</u></em>

kotegsom [21]3 years ago
4 0

Answer:

(5,2)

Step-by-step explanation:

you need to go two half way from the farthest point from the left to the right so that would be from 2 to 8 which is a distance of 6 so you go halfway over and that puts you at 5 then you find the distance from the lowest point to the highest point which goes from -2 to 6 with a distance of 8 so that means you go up for which puts you at 2 which means the center of the triangle is at the point (5, 2)

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