Question

Find the value of y for which the distance between the points A (3,-1) B (11,y) equal to 10 units

Answer 1

is given that the distance between the points AB = 10. 
Therefore, AB= √(11-3)2 + (y+1)2  = 10

                       = √82 + (y+1)2 =10

                      = √64+(y+1)2  =10
Squaring on both sides, we get,

  64 +(y+1)2 = 100

64+ y2 + 2y + 1 = 100

y2 + 2y +1 = 100-64=36

y2+2y - 35 = 0

Now, by splitting the middle term method, we get,

y2+ 7y - 5y - 35= 0

y(y+7) -5(y+7)

(y-5) ( y+7)

y = 5 or y = -7

Therefore, the value of 'y' can be either 5 or -7.

Hope it helps.  :)

Answer 2

Answer:

Step-by-step explanation:

AB=√(3-11)^2 +(-1-Y)^2

10=√64 +(1+Y)^2. (SQUARING)

100= 64 +(1+Y)^2

36=(1+Y)^2. (ROOTING)

Plus minus 6 is equal to y plus 1 so y is equal to 5,-7