If p(2,p)is the mid point of line segment joining the point A(6,-5)and B(-2,11)find the value of p

If p(2,p)is the mid point of line segment joining the point A(6,-5)and

1.	If p(2,p)is the mid point of line segment joining the point A(6,-5)and B(-2,11)find the value of p
Answer» GIVEN points are P(2,p), A(6,-5) , B(-2,11)P is the mid point of A & Bfor distance AP : x1= 6 ,y1= -5 , x2 = 2, y2= pAP =√(x1 - x2)² + (y1 - y2)²[ By Distance formula]AP =√[(6 -2)]² + (-5 - p)²AP = √(4)² + [(-5)² +p² +2×5p]AP = √ 16+ [25 +p² +10p]AP = √ 16 + 25 +p² +10pAP = √41 +p² +10pFor distance BP: x1 = -2 ,y1= 11, x2= 2, y2 = pBP=√(-2 -2)² + (11 - p)²= √(-4)² + [(11)² +p² -2×11p]= √ 16 + [121 +p² - 22p]= √ 16 +121 +p² - 22pBP = √137 +p² -22pATQ,AP = BP√41 +p² +10p = √137 +p² -22p[On squaring both sides]41 -137 +p² -p² +10p +22p = 0-96 +32p = 032p = 96p = 96/32p = 3Hence, the value of p is 3. Value of p is 3 The value of p is 3.