Consider the triangle OAB where ' O is the origin.If B=(3 4) and orthocentre of the triangle is P=(1 4) find the coordinates of A .
Answers
Answer:
What will be the orthocentre of a triangle whose vertices are (0,0),(3,4),(4,0)?
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Triangle ABC, vertices are A(3,4), B(0,0), C(4,0)
O is the Orthocentre of the triangle
By considering the coordinates of B, C, A ,we can conclude that:
Equation of BC is y=0………..(1)
Equation of AD is x=3 ………..(2)
As we know slope of BC(being on the Xaxis) = 0
And for a vertical line AD, however the slope is not defined. It does not have a slope.
We take the slope of AC = (4–0)/(3–4) = 4/-1 = -4
So, the slope of its perpendicular(BE) has to be its negative reciprocal. That is the slope of BE = 1/4
So, equation of BE, which is passing through (0,0) has to be y= mx + b , where m = 1/4, x=0, y=0
=> 0= 1/4*0 + b
=> b=0
So, BE is y= 1/4*x +0
=> y = x/4
Now, by solving
x=3………..(1)
y= x/4 ………..(2)
We get y = 3/4
So, Orthocentre coordinates are (3, 3/4)