Answer:
Explanation:
Given points,
Using mid-point formula,
[tex] \boldsymbol{ = \dfrac{x_1 + x_2}{2} \: \dfrac{y_1 + y_2}{2} }[/tex]
Where,
Substituting the given coordinates,
[tex] = \bigg( \dfrac{[2 + 12]}{2},\: \dfrac{[3 + 7]}{2} \bigg)[/tex]
[tex] = \bigg( \dfrac{14}{2},\: \dfrac{10}{2} \bigg)[/tex]
[tex] = \big( 7,\: 5 \big)[/tex]
∴ Midpoint of P, Q is (7, 5)
[tex]\clubsuit[/tex] Mid-Point Formula :
[tex]\bigstar \: \: \sf\boxed{\bold{Mid-Point =\: \bigg[\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg]}}\: \: \: \bigstar\\[/tex]
where,
Given Co-ordinates :
[tex]\leadsto \sf P(2 , 3)[/tex]
[tex]\leadsto \sf Q(12 , 7)[/tex]
According to the question by using the formula we get,
[tex]\implies \bf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{2 + 12}{2} , \dfrac{3 + 7}{2}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{\cancel{14}}{\cancel{2}} , \dfrac{\cancel{10}}{\cancel{2}}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{7}{1} , \dfrac{5}{1}\bigg\}\\[/tex]
[tex]\implies \sf\bold{Mid-Point_{(P, Q)} =\: (7 , 5)}\\[/tex]
[tex]\therefore[/tex] The mid-point of the co-ordinates of the line PQ is (7 , 5) .
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Answers & Comments
Answer:
Explanation:
Given points,
Using mid-point formula,
[tex] \boldsymbol{ = \dfrac{x_1 + x_2}{2} \: \dfrac{y_1 + y_2}{2} }[/tex]
Where,
Substituting the given coordinates,
[tex] = \bigg( \dfrac{[2 + 12]}{2},\: \dfrac{[3 + 7]}{2} \bigg)[/tex]
[tex] = \bigg( \dfrac{14}{2},\: \dfrac{10}{2} \bigg)[/tex]
[tex] = \big( 7,\: 5 \big)[/tex]
∴ Midpoint of P, Q is (7, 5)
________________________________
Answer:
Given :-
To Find :-
Formula Used :-
[tex]\clubsuit[/tex] Mid-Point Formula :
[tex]\bigstar \: \: \sf\boxed{\bold{Mid-Point =\: \bigg[\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg]}}\: \: \: \bigstar\\[/tex]
where,
Solution :-
Given Co-ordinates :
[tex]\leadsto \sf P(2 , 3)[/tex]
[tex]\leadsto \sf Q(12 , 7)[/tex]
where,
According to the question by using the formula we get,
[tex]\implies \bf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{2 + 12}{2} , \dfrac{3 + 7}{2}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{\cancel{14}}{\cancel{2}} , \dfrac{\cancel{10}}{\cancel{2}}\bigg\}\\[/tex]
[tex]\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{7}{1} , \dfrac{5}{1}\bigg\}\\[/tex]
[tex]\implies \sf\bold{Mid-Point_{(P, Q)} =\: (7 , 5)}\\[/tex]
[tex]\therefore[/tex] The mid-point of the co-ordinates of the line PQ is (7 , 5) .