LS and y-axis intersection

In what ratio is the line segment joining P (5, 3) and Q (–5, 3) divided by the y-axis? Also, find the coordinates of the intersection point.

Correct answer:

x =  0
y =  3
r =  1:1

Step-by-step explanation:

P=(5,3) Q=(−5,3)  y=f(x)=k⋅ x+q  Py​=k⋅ Px​+q Qy​=k⋅ Qx​+q 3=k⋅ 5+q 3=k⋅ (−5)+q  5k+q=3 5k−q=−3  Row2−Row1→Row2 5k+q=3 −2q=−6  q=−2−6​=3 k=53−q​=53−3​=0  k=0 q=3  y−ax​is: x=0 I=(x,y) I = y−ax​is ∩ PQ  x=0 y=k⋅ x+q=0⋅ 0+3=3
I=(x,y)  a=dist(I,P)=∣IP∣=(Ix​−Px​)2+(Iy​−Py​)2​=(0−5)2+(3−3)2​=5 b=dist(I,Q)=∣IQ∣=(Ix​−Qx​)2+(Iy​−Qy​)2​=(0−(−5))2+(3−3)2​=5  r=a:b=5:5=1:1=1

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