Maths / Coordinate Geometry / Mid Point Formula

QUESTION

(3, 4-a) is the mid-point of the lines segment joining points (2, a) and (4, 2). What is the value of a ?

 OPTIONS A. 1 B. 8 C. -4 D. 2
Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

For the mid point

$\dpi{120} \fn_jvn \large x=\frac{x_1+x_2}{2}\: and\: y=\frac{y_1+y_2}{2}$

$\dpi{120} \fn_jvn \large \dpi{120} \fn_jvn \large x=\frac{2+4}{2}\: and\: y=\frac{a+2}{2}$

$\dpi{120} \fn_jvn \large x=\frac{6}{2}\: and\: y=\frac{a+2}{2}$

$\dpi{120} \fn_jvn \large The \: coordinates \: are (3,\frac{a+2}{2})$

$\dpi{120} \fn_jvn \large \large \frac{a+2}{2}=4-a \Rightarrow a+2=8-2a\Rightarrow a+2a=8-2\Rightarrow 3a=6\Rightarrow a=2$

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