Find the cordinates of yhe orthocentre ofbthe triangle whose vertices are (0,0),(6,0)
Answers
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)