The point on the x-axis which is equidistant form (-4, 0) and (10, 0) is ________________ Plz tell me the answer, it is so important
Answers
Given: Two points : (-4,0) and (10,0)
To find: A point which is equidistant from both the given points.
Solution:
Now, we know that the point is on x axis (given in the question),
So the y co-ordinate will be 0, y = 0
So, Let the point be (x,0)
The distance formula is \sqrt{(x-x1)^2 + (y-y1)^2}
(x−x1)
2
+(y−y1)
2
Here x1 is -4 and y1 is 0
Then the distance of (x, 0) from the point (- 4, 0) will be,
= \sqrt{(x+4)^2 + (0-0)^2}
(x+4)
2
+(0−0)
2
= √(x+4)²
Now, the distance of (x, 0) from the point (10, 0) will be
\sqrt{(x-10)^2 + (0-0)^2}
(x−10)
2
+(0−0)
2
= √(x - 10)²
By the given condition, equating the both distance, we get
√(x+4)² = √(x - 10)²
squaring both sides, we get
(x+4)² = (x - 10)²
x² + 8x +16 = x² - 20x + 100
28x = 84
x = 84/28
x = 3
Answer:
So the point is (D) (3,0).