Point P(3, 2) lie on the line
x = 2y
x = y
2x - 1 = y
x = y + 1
Answers
Answer:
its easy
Step-by-step explanation:
Here the line through P(2,−3) intersect both lines at A and B respectively. And P divides AB externally in ratio 3:2=m:n, So P is the external point .
Hence using the section formula;
2=
3−2
3x
2
−2x
1
⇒3x
2
−2x
1
=2⟶(1)
and,−3=
3−2
3y
2
−2y
1
⇒3y
2
−2y
1
=−3⟶(2)
Also, (x
1
,y
1
) and (x
2
,y
2
) satisfies the line x−2y+7=0 and x+3y−3=0
so, x
1
−2y
1
+7=0⟶(3)
and, x
2
−3y
2
−3=0⟶(4)
adding (3) and (4) we get,
x
1
+x
2
+(3y
2
−2y
1
)=−4
⇒x
1
+x
2
−3=−4(from(2))
⇒x
1
+x
2
=−1⟶(5)
solving (5) and (1) we get, x
1
=−1;x
2
=0
and by using the value in above equation we get, y
1
=3;y
2
=1
∴A=(−1,3);B=(0.1)
Hence the equation of AB is given as;
(y−3)=(
−1−0
3−1
)(x+1)
⇒y+2x−1=0