Question

Q1. Two points A (-2, 9) and B (4, 8) lie on a line l.

(i) Find the slope of the line l.

(ii) Find the coordinates of the midpoint of the points A and B

(iii) Find the distance between points A and B.
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Answer 1

$Given \: two \:points \: A(-2,9) \:and \: B(4,8)$

$lie \:on \:a \:line .$

$Let \:(x_{1} , y_{1}) = A(-2,9) \:and$

$(x_{2} , y_{2}) = B(4,8)$

$1.) \red{Slope \: of \:the \:line (AB) }$

$= \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$= \frac{ 8 - 9}{4-(-2)}$

$= \frac{-9}{4+2}$

$= \frac{-9}{6}$

$\green{ = \frac{-3}{2}}$

$2)\red{Mid \:point \:of \: joining \: points \: A \:and \:B}$

$= \Big( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\Big)$

$= \Big( \frac{-2+4}{2}, \frac{9+8}{2}\Big)$

$= \Big( \frac{2}{2} , \frac{17}{2}\Big)$

$\green {= \Big( 1 , \frac{17}{2}\Big)}$

$3.) \red{ Distance \:of \: AB}$

$= \sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} )}$

$= \sqrt{ [ 4-(-2)]^{2} + ( 8-9)^{2} }$

$= \sqrt{ ( 4+2)^{2} + (-1)^{2} }$

$= \sqrt{ 6^{2} + 1 }$

$= \sqrt{36 + 1 }$

$\green {= \sqrt{37}}$

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