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If the distance between the points (3, 0) and (0, y) is 5 units. y is positive then what is value of y?
- a)3
- b)2
- c)4
- d)1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the distance between the points (3, 0) and (0, y) is 5 units. y is ...
To find the value of y, we need to calculate the distance between the points (3, 0) and (0, y) and equate it to 5 units.
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Given Points:
Point A: (3, 0)
Point B: (0, y)
Calculating the Distance:
Using the distance formula, we can calculate the distance between points A and B as follows:
d = √((0 - 3)^2 + (y - 0)^2)
= √(9 + y^2)
Given that the distance between the points is 5 units, we can set up the equation:
5 = √(9 + y^2)
Solving the Equation:
To solve the equation, we need to isolate y. Squaring both sides of the equation, we get:
25 = 9 + y^2
Subtracting 9 from both sides, we have:
16 = y^2
Taking the square root of both sides, we obtain:
y = ±4
Since y is stated to be positive, the value of y is 4.
Therefore, the correct answer is option 'C' (4).
Distance Formula:
The distance between two points (x1, y1) and (x2, y2) in a coordinate plane can be calculated using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Given Points:
Point A: (3, 0)
Point B: (0, y)
Calculating the Distance:
Using the distance formula, we can calculate the distance between points A and B as follows:
d = √((0 - 3)^2 + (y - 0)^2)
= √(9 + y^2)
Given that the distance between the points is 5 units, we can set up the equation:
5 = √(9 + y^2)
Solving the Equation:
To solve the equation, we need to isolate y. Squaring both sides of the equation, we get:
25 = 9 + y^2
Subtracting 9 from both sides, we have:
16 = y^2
Taking the square root of both sides, we obtain:
y = ±4
Since y is stated to be positive, the value of y is 4.
Therefore, the correct answer is option 'C' (4).
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Community Answer
If the distance between the points (3, 0) and (0, y) is 5 units. y is ...
(3 - 0)2 + (0 - y)2 = 52
9 + y2 = 25 ⇒ y2 = 16 ⇒ y = ± 4
y is positive, ∴ y = 4
9 + y2 = 25 ⇒ y2 = 16 ⇒ y = ± 4
y is positive, ∴ y = 4
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