the points A(2,3) B(2,5) and ____ are colinear
a) (1,1)
b) (3,0)
c) (2,-4)
d) (0,5)
Answers
For 3 points to be collinear,it must satisfy the equation:
AB+AC=BC
Here we only have A(2,3) and B(2,5), so we have to assume third point as C(x,y)
Now,find the value of AB,AC and BC
AB=√(2-2)²+(5-3)²
=√4
=2
AC=√(x-2)²+(y-3)²
=√x²+4-4x+y²+9-6y
=√x²+13-4x+y²-6y
=√x²+y²-4x-6y+13
BC=√(x-2)²+(y-5)²
=√x²+4-4x+y²+25-10y
=√x²+y²-4x-10y+29
Now,put the value in equation AB+AC=BC,you will get your answer.
AB+AC=BC
2+√x²+y²-4x-6y+13 =√x²+y²-4x-10y+29
Squaring on both sides:
(2+√x²+y²-4x-6y+13)²=(√x²+y²-4x-10y+29)²
Here we write it in form (a+b)²=a²+b²+2ab
(2²+x²+y²-4x-6y+13) +4√x²+y²-4x-6y+13=x²+y²-4x-10y+29
=4+x²+y²-4x-6y+13+4√x²+y²-4x-6y+13=x²+y²-4x-10y+29
=4-6y+13+4√x²+y²-4x-6y+13=29-10y
=4√x²+y²-4x-6y+13=29-10y-17+6y
=4√x²+y²-4x-6y+13=12-4y
=4√x²+y²-4x-6y+13=4(3-y)
=√x²+y²-4x-6y+13=3-y
=x²+y²-4x-6y+13=9+y²-6y
=x²-4x+13=9
=x²-2x-2x+4
=x(x-2)-2(x-2)
=x=2
Here we got x=2,now see in the option,the third option c has 2,so that is your correct answer.
I have put so much effort in writing this,i will be happy if you can understand the answer properly.It took almost half an hour..oh
You can write it in your copy and try to understand.
Answer:
c is the right answer
Step-by-step explanation:
hope it helps you and please make my answer as brainlist answer