P(3,2) and Q(7,7) are two points.Perpendiculars are drawn x axis from P and Q meeting the x-axis at L and M respectively. Find the co-ordinates of L and M and find the length of L and M

Dear Student,

Please find below the solution to the asked query:

Given : P ( 3 , 2 ) and Q ( 7 , 7 ) are two points.Perpendiculars are drawn x axis from P and Q meeting the x-axis at L and M respectively.

So,

Coordinate of L = ( 3 , 0 )  and coordinate of M  = ( 7 , 0 )

We know distance formula :  d = $\sqrt{{\left(x_2 - x_{1 }\right)}^2 + {\left(y_2 - y_{1 }\right)}^2}$

For length of PL , x ₁ = 3 ,  y₁ = 2  and x ₂ = 3 ,  y₂ = 0 , So

PL = $\sqrt{{\left(3 - 3\right)}^2 + {\left(0 - 2\right)}^2} = \sqrt{0^2 + {\left( - 2\right)}^2} = \sqrt{4} =\mathbf{ }\mathbf{2}\mathbf{ }\mathbf{unit}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$

And

For length of QM , x ₁ = 7 ,  y₁ = 7  and x ₂ = 7 ,  y₂ = 0 , So

QM = $\sqrt{{\left(7 -7\right)}^2 + {\left(0 - 7\right)}^2} = \sqrt{0^2 + {\left(- 7\right)}^2} = \sqrt{49} = \mathbf{ }\mathbf{7}\mathbf{ }\mathbf{ }\mathbf{unit}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$
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