Question

,distance between two points is (5,-2) and (1,a) is 5. find the value of a

Answer 1

To find the value of 'a', we use the distance formula with the given points (5, -2) and (1, a), resulting in two possible values for 'a': 1 or -5.

Step-by-step explanation:

The question asks to find the value of a in the coordinates (1,a) given the distance between two points, (5, -2) and (1, a), which is 5 units. The distance can be calculated using the Pythagorean theorem which in two dimensions is √((x2 - x1)^2 + (y2 - y1)^2). Here, the two points are (5, -2) and (1, a).

To find the value of a, we can set up the equation based on the distance formula:

1. Subtract the x-coordinates: 5 - 1 = 4, and square the result: 4^2 = 16.
2. Subtract the y-coordinate of the first point from a, square the result and equate it to 5^2 (since the distance is 5 units): (-2 - a)^2 = 25 - 16.
3. Simplify to find the value of a: (-2 - a)^2 = 9.
4. Take the square root: -2 - a = ±3(3).
5. Solve for a to get two possible solutions: a = -2 + 3 or a = -2 - 3, which simplifies to a = 1 or a = -5.

Therefore, the possible values for a are 1 or -5.