Question

orthocentre of triangle with vertices (0,0) (3,4) (4,0)

Answer 1

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)

Answer 2

Answer:

In 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)