If the mid point (x,y) of the line joining (3,4) and (p,7) lies on 2x+2y+1=0, then what will be the value of p?
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vikram5767:
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★ Method of Solution : ✯
Given : If the mid point (x,y) of the line joining (3,4) and (p,7) lies on 2x+2y+1=0,
Let A and B vertices of their points!
Here, A = (3,4). and B = (P,7)
Now, According to the Question's Statement!
Statement : If the mid point (x,y) of the line joining (3,4) and (p,7) lies on 2x+2y+1=0,
We know that Midpoint Formula of Coordinate Geometry!
Midpoint Formula : { x1 + x2 / 2 , Y1 + Y2/2 }
Substituting the obtained value on Formula!
Midpoint Formula : { x1 + x2 / 2 , Y1 + Y2/2 }
( x , y ) = (3+ p / 2 ) , ( 4 + 7 / 2)
x = 3 + p / 2 , or y = ( 4+7/2)
•°• x = 3 + p/ 2 or y = 11 /2
Here, Value of x and y are (3+p) and 11 respectively!
Equation : 2x+2y+1=0,
→ 2 ( 3 + p/2 ) + 2 (11/2) + 1 = 0
→ 3 + p + 11 + 1 = 0
→ p + 3 + 12 = 0
→ p + 15 = 0
→ p = - 15
•°• p = -15
Hence, Required Value of p is (-15).
Given : If the mid point (x,y) of the line joining (3,4) and (p,7) lies on 2x+2y+1=0,
Let A and B vertices of their points!
Here, A = (3,4). and B = (P,7)
Now, According to the Question's Statement!
Statement : If the mid point (x,y) of the line joining (3,4) and (p,7) lies on 2x+2y+1=0,
We know that Midpoint Formula of Coordinate Geometry!
Midpoint Formula : { x1 + x2 / 2 , Y1 + Y2/2 }
Substituting the obtained value on Formula!
Midpoint Formula : { x1 + x2 / 2 , Y1 + Y2/2 }
( x , y ) = (3+ p / 2 ) , ( 4 + 7 / 2)
x = 3 + p / 2 , or y = ( 4+7/2)
•°• x = 3 + p/ 2 or y = 11 /2
Here, Value of x and y are (3+p) and 11 respectively!
Equation : 2x+2y+1=0,
→ 2 ( 3 + p/2 ) + 2 (11/2) + 1 = 0
→ 3 + p + 11 + 1 = 0
→ p + 3 + 12 = 0
→ p + 15 = 0
→ p = - 15
•°• p = -15
Hence, Required Value of p is (-15).
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