Answer
y= 0 or 2
Both the values satisfy distance condition.
Work Step by Step
To find y, we will calculate distance between given points, i. e. (7, y) and (3, 3), using distance formula and equate it to the given distance i.e. 5. Thus-
$ \sqrt { (x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2}}$ = 5
$ \sqrt { (3 - 7) ^{2} + (3- y) ^{2}}$ = 5
$ \sqrt { (-4) ^{2} + (9 -2y + y^{2}) }$ = 5
Squaring on both sides, we get-
$ { 16 + (9 -2y + y^{2})}$ = $25$
$ y^{2}-2y + 25$ = $25$
OR
$ y^{2}-2y$ = 0
( adding -25 on both sides)
$y (y- 2)$ = 0 (On factorizing)
Equating each factor to zero, we get-
$y$= 0 or 2
Therefore y may be 0 or 2
