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Find X If Distance Between Points L(X, 7) and M(1, 15) is 10. - Geometry

Sum

Find x if distance between points L(x, 7) and M(1, 15) is 10. 

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Solution

Distance between LM = 10

\[LM = \sqrt{\left( x - 1 \right)^2 + \left( 7 - 15 \right)^2} = 10\]

\[ \Rightarrow \sqrt{\left( x - 1 \right)^2 + \left( - 8 \right)^2} = 10\]

\[ \Rightarrow \sqrt{\left( x - 1 \right)^2 + 64} = 100\]

Squaring both sides

\[\left( x - 1 \right)^2 + 64 = 100\]

\[ \Rightarrow x^2 - 2x + 1 + 64 = 100\]

\[ \Rightarrow x^2 - 2x - 35 = 0\]

\[ \Rightarrow x^2 - 7x + 5x - 35 = 0\]

\[ \Rightarrow x\left( x - 7 \right) + 5\left( x - 7 \right) = 0\]

\[ \Rightarrow \left( x + 5 \right)\left( x - 7 \right) = 0\]

\[ \Rightarrow x = - 5, 7\]

Concept: Distance Formula
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APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 5 Co-ordinate Geometry
Practice Set 5.1 | Q 7 | Page 108
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