Asked by liam

point A(-1,-2) B(7,2) C(k,4) K is a constant. The vertices of ABC. Angle ABC is a right angle.

Ive worked out the gradient of AB to be 1/2.

How do you calculate the value of k??

thanks for the help
Answered by Reiny
slope of AB = 1/2 , you had that
slope of BC = 2/(k-4)

since angle B is 90°, the above slopes must be negative reciprocals of each other, that is ....

2/(k-4) = -2

solve for k
Answered by liam
sorry but confused
Answered by Reiny
confused about what ?

The property of slopes of perpendicular lines , or
the procedure to solve the equation ?
Answered by liam
where you get slope of BC = 2/(k-4) from??
Answered by Duffy
As BC is perpendicular to AB, being a right angled triangle. The gradient of BC would be -2.
For the equation of BC,
y-2=-2(x-7)
y-2=-2x+14
2x+y=16
Then put C(k,4) as x and y,
2(k)+(4)=16
2k+4=16
2k=16-4
2k=12
k=6


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