The point P5-2 is the mid point of line segment joining the Ax2- y-12 and Bx-1- y-3 then find the value of x y-

Let #10;given points be #10; #10; A( #10;x2,y + 12),B( x + 1,y 3 #10;) and P( 5, 2) #10; #10;Since, #10; P is midpoint of line seg ...

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Standard X

Mathematics

Section Formula

The point P...

Question

The point $P (5, - 2)$ is the mid point of line segment joining the $A (\frac{x}{2}, \frac{y + 1}{2})$ and $B (x + 1, y - 3)$ then find the value of $x$ & $y$ .

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Solution

Let given points be

$A (\frac{x}{2}, \frac{y + 1}{2}), B (x + 1, y - 3) a n d P (5, - 2)$

Since, $P$ is midpoint of line segment AB

$\frac{\frac{x}{2} + x + 1}{2} = 5$

$\frac{x}{2} + x + 1 = 10$

$\frac{3 x}{2} = 9$

$x = 6$

and

$\frac{\frac{y + 1}{2} + y - 3}{2} = - 2$

$\frac{y + 1}{2} + y - 3 = - 4$

$\frac{y + 1 y + 2 y}{2} = - 1$

$3 y + 1 = - 2$

$3 y = - 3$

$y = - 1$

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The point P(5,−2) is the mid point of line segment joining the A(x2,y+12) and B(x+1,y−3) then find the value of x & y.

Let given points be A(x2,y+12),B(x+1,y−3)andP(5,−2) Since, P is midpoint of line segment AB x2+x+12=5 x2+x+1=10 3x2=9 x=6 and y+12+y−32=−2 y+12+y−3=−4 y+1y+2y2=−1 3y+1=−2 3y=−3 y=−1

The point $P (5, - 2)$ is the mid point of line segment joining the $A (\frac{x}{2}, \frac{y + 1}{2})$ and $B (x + 1, y - 3)$ then find the value of $x$ & $y$ .