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8. Find the value of m if the distance between the points \left( m,-4 \right) and \left( 3,2 \right) is 3\sqrt{5} units.
Class 10 | Distance and Section Formulae | Frank | ICSE | Maths
8. Find the value of m if the distance between the points \left( m,-4 \right) and \left( 3,2 \right) is 3\sqrt{5} units.

Distance – The length along a line or line segment between two points on the line or line segment.

Section formula define – The section formula helps in finding the coordinates of a point dividing the coordinates of a point dividing a given line segment into two parts such that their lengths are in a given ratio.

Solution:-

From the question it is given that,

The distance between the points \left( m,-4 \right) and \left( 3,2 \right), assume the two points be A and B respectively.

AB=3\sqrt{5}units

\sqrt{\left( {{\left( m-3 \right)}^{2}}+{{\left(-4-2 \right)}^{2}} \right)}=3\sqrt{5}

Now, squaring on both side we get,

{{\left( m-3 \right)}^{2}}+{{\left( -4-2 \right)}^{2}}=45

\left( {{m}^{2}}+9-6m \right)+\left( 16+4+16 \right)=45

{{m}^{2}}+9-6m+36=45

By transposing we get,

{{m}^{2}}-6m+45-45=0

{{m}^{2}}-6m=0

Now, take out common in above terms we get,

m\left( m-6 \right)=0

m=0,m-6=0

m=0,m=6.

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