The points (4,2) and (-1,y) are sqrt(74) units apart. What is the value of y?

Question

question: The points (4,2) and (-1,y) are sqrt(74) units apart. What is the value of y?

p.s. sqrt(74) means square root of 74

i have no idea what so ever how to get this...and can you please show me the process so i can get the other ones.
thank you =]

Answer 1

It's just the distance formula:

d = √((x1 - x2)² + (y1 - y2)²)

In this case, d = √74, (x1, y1) = (4, 2), and (x2, y2) = (-1, y).

√74 = √((4 - -1)² + (2 - y)²)

Square both sides to get rid of the radicals:

74 = 5² + (2 - y)²

Simplify:

74 = 25 + (2 - y)²

49 = (2 - y)²

Take the square root of both sides, remembering to do both the pos and neg square root:

± 7 = (2 - y)

Add y to both sides and subtract ±7 from both sides:

y = 2 ± 7

So y = 9 or y = -5

Answer 2

the area formula is d = sqrt( (y2-y1)^2+(x2-x1)^2) seventy 4 = (y - 2)^2 + (-a million-4)^2 seventy 4 = (y-2)^2 + 25 40 9 = (y-2)^2 +/- 7 = y - 2 y = -5 OR 9 Tiku's answer become superb and known, yet i assumed you're able to make the main of a sprint greater explanation.

Answer 3

you just have to use the following procedure

(x1 - x2 )^2 + (y1 - y2)^2 = d^2

In this case you can take as your first point

(x1,y1) = (4,2)

and the second one

(x2,y2) = (-1,y)

and d = sqrt(74), then

(4 - {-1} )^2 + (2 - y)^2 = 74
5^2 + (2 - y)^2 = 74
(2 - y)^2 = 49

and you take sqrt at both sides

2 - y = +/- 7

the +/- is because if you make (7)^2 you obtain the same result as if you make (-7)^2

the next thing is just to isolate y to give

y = 2 -/+ 7

or y = 2 - 7 = -5 is one solution and other valid solution is y = 2 + 7 = 9.

Answer 4

(4--1)^2 + (2-y)^2 = 74

(2-y)^2 = 74-25 = 49

2-y = 7
y = -5

2-y = -7
y = 9