given A(a,2) B(3,4) and C(-2,1). if A is at the same distance to the point B and C find a
Use distance formula (point-to-point):
d = sqrt((y2 - y1)^2 + (x2 - x1)^2)
where (x1,y1) and (x2,y2) are the points involved.
In the problem, it was said that the distances from A -> B and A -> C are equal. Therefore,
sqrt((4 - 2)^2 + (3 - a)^2) = sqrt((1 - 2)^2 + (-2 - a)^2)
Squaring both sides to remove the squareroot sign:
(4 - 2)^2 + (3 - a)^2 = (1 - 2)^2 + (-2 - a)^2
(-2)^2 + (3 - a)^2 = (-1)^2 + (-2 - a)^2
4 + 9 - 6a + a^2 = 1 + 4 + 4a + a^2
13 - 6a = 5 + 4a
-6a - 4a = 5 - 13
-10a = -8
a = 4/5
Hope this helps~ `u`
tnx
To find the value of 'a' when point A is equidistant from points B and C, we need to use the distance formula.
The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Since we need to find the distance between A and B, as well as A and C, we can set up the equations as follows:
√((3 - a)² + (4 - 2)²) = √((-2 - a)² + (1 - 2)²)
Simplifying both sides of the equation:
√((3 - a)² + 4) = √((-2 - a)² + 1)
Squaring both sides to eliminate the square root:
((3 - a)² + 4) = ((-2 - a)² + 1)
Expanding and rearranging the equation:
(a² - 6a + 9 + 4) = (a² + 4a + 4 + 1)
Simplifying and combining like terms:
a² - 6a + 13 = a² + 4a + 5
Subtracting a² from both sides to eliminate the quadratic term:
-6a + 13 = 4a + 5
Moving all the variables to one side of the equation:
-6a - 4a = 5 - 13
Combining like terms:
-10a = -8
Dividing both sides of the equation by -10:
a = -8 / -10
Simplifying:
a = 4/5
Therefore, the value of 'a' is 4/5.