Posted by Jake on Friday, January 21, 2011 at 3:18pm.
Find the value of the constant t such that the triangle formed by A (2,2) ,B (4,-5) ,C (6,t) is right angled at B(4,-5).
Math - MathMate, Friday, January 21, 2011 at 9:54pm
Line passing through two given points P1(x1,y1) and P2(x2,y2)
L: (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
or (x2-x1)(y-y1) = (y2-y1)(x-x1)
For line AB:
AB: (4-2)(y-2) = (-5-2)(x-2)
=> AB: 2(y-2) = (-7)(x-2)
=> AB: y = -3.5x + 9
Similarly, line BC is:
=> BC: y=((t+5)/2)x - 2t-15
If the two lines are to be perpendicular to each other, the product of the slopes must be -1, or
-3.5*(t+5)/2 = -1
Solve for t to get t=-31/7
Slope of AB: (-5-2)/(4-2)=-3.5
Slope of BC: (-31/7+5)/(6-4)= 2/7
Product of slopes : -3.5*2/7=-1 OK
Answer This Question
More Related Questions
- Math - The Perimeter of a right angled triangle is 40 CM. Find the area of the ...
- math - (please explain with brief explanation) The sides of an equilateral ...
- Math - A right-angled triangled has sides (x+10)cm,(x+2)cm and (x+4). find the ...
- math - Triangle ABC is right-angled at B. Segment BD is an altitude of the ...
- math - The sides of a right angled triangle are x,x+1 and x+2.find x,Am not ...
- math - The difference of two acute angles in a right angled triangle is 2?/5....
- math - B . . . . . . . . . . . . . . C A Triangle ABC is right angled at A. The ...
- mathematics - an equilateral triangle is placed inside and a right angled ...
- math - the base of right angled triangle measures 48 cm and its hypotenuse is 50...
- maths-urgently needed - In right angled triangle ABC angle B=90 degree and AB= ...