Question

The vertices of triangle ABC are A = (1,6) B=4,6), C=(6 ,14), AD
is the bisector of Angle A and meets BC at D. Find
the coordinates of point D.​

Answer 1

Answer:

Step-by-step explanation:

Length of AC =  √ [ ( 1 - 6 )² + ( 6 - 14 )² ] = √ [ 89 ]

Similarly AB = Sqrt of [ ( 1 - 4 )² + ( 6 - 6 )² ] =  3

We also know that AB * CD  =  AC * BD

=>  3 * CD = √(89) * BD

=> CD/BD  =  √(89)/3

It means D divides BC in the ratio = √(89) : 3

We can now find coordinates of D knowing coordinates of B and C. easily.