Three points have coordinates A(1,2), B(9,0) and C(6,t). Calculate the value(s) of t if : (a) ∠ABC=90∘ (b) AC is perpendicular to BC?

1 Answer
Shwetank Mauria
Feb 6, 2018

(a) t=−12 and (b) t=5 or t=−3

Explanation:

Slope of line joining (x1,y1) and (x2,y2) is y2−y1x2−x1

Therefore slope of AB is 0−29−1=−28=−14,

slope of BC is t−06−9=−t3 and

slope of AC is t−26−1=t−25.

Further if two lines are perpendicular, product of their slopes is −1

Hence (a) if ∠ABC=90∘, we have AB perpendicular to BC i.e. −14×(−t3)=−1

or t12=−1 i.e. t=−12

(b) if AC is perpendicular to BC, then

t−25×(−t3)=−1 i.e. t(t−2)=15

or t2−2t−15=0 or (t−5)(t+3)=0 i.e. t=5 or t=−3

Related questions
Impact of this question
1714 views around the world
You can reuse this answer
Creative Commons License