Question

The equation x + 2y = 3
represents the side BC of
AABC;where co-ordinates of
Aare (1,2). If the x-coordinate
of the orthocenter of AABC İS

3 the y-coordinates of the
orthocenter is:​

Answer 1

Given :  The equation x + 2y = 3  represents the side BC of  ΔABC .  co-ordinates of  A are (1,2) .  x-coordinate  of the orthocenter of ΔABC İs 3  

To Find :  y-coordinates of the  orthocenter

Solution:

BC   x + 2y  = 3

=> 2y = -x  + 3

=> y = -x/2  + 3/2

Slope of BC  = -1/2

Altitude Slope   :  -1/(-1/2)  = 2

Passes through A ( 1 , 2)

y  - 2   = 2 ( x -  1)

=> y - 2  = 2x  - 2

=>  y = 2x

x-coordinate  of the orthocenter   is 3

=> y  = 2 (3)

=> y = 6

y-coordinates of the  orthocenter is  6

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