Find the value of a for which the point P(a,2) is the midpoint of the line segment joining the point q(-5,4)and r(-1,0)
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given P(a,2) is a midpoint of the line segment joining Q(-5,4) and R(-1,0)
hence distance of QP= distance of PR
=> (a-(-5))^2 +(2-4)^2= (-1-a)^2+ (0-2)^2
=> (a+5)^2+ 4=(-(a+1))^2+4
=> a^2+ 10 a+ 25= a^2+ 2 a+1
=> 10a- 2a= 1-25
=> 8 a= - 24
=> a= -24/8
a= -3
hope this helps
hence distance of QP= distance of PR
=> (a-(-5))^2 +(2-4)^2= (-1-a)^2+ (0-2)^2
=> (a+5)^2+ 4=(-(a+1))^2+4
=> a^2+ 10 a+ 25= a^2+ 2 a+1
=> 10a- 2a= 1-25
=> 8 a= - 24
=> a= -24/8
a= -3
hope this helps
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