If line AB have midpoint (1,2) and gradient 0 with distance of 10 units find the coordinates of A and B
hint: gradient 0 means y never changes.
Yeah i know but i can not find the coordinates of A and B. when i satisify midpoint distance is not satisfied and vice versa...
Did you try actually plotting the line segment? Just plot (1,2) and then go 5 left and 5 right.
A=(-4,2) B=(6,2)
Oh thnks another query is that if the information is same but gradient is 3/4 then??
To find the coordinates of point A and B on the line AB, we can use the midpoint formula and the given information about the gradient and the distance.
1. Let's start by finding the coordinates of the midpoint of line AB, which is given as (1, 2). The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
So, we can write:
(x₁ + x₂)/2 = 1
(y₁ + y₂)/2 = 2
2. We are also given that the gradient (or slope) of the line is 0. The slope-intercept form of a linear equation is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = 0x + c = c. This means that the line is a horizontal line with a constant y-coordinate.
3. We know that the distance between points A and B is 10 units. Since the line is horizontal, the difference between the x-coordinates of A and B will be 10 units.
4. Using the midpoint formula, we can substitute the values we know to find the coordinates of the endpoints, A and B.
From the first equation: (x₁ + x₂)/2 = 1
Since the line is horizontal, we know that y₁ = y₂ (the y-coordinates of A and B are the same). Substituting y₁ = y₂ = y, we get:
(x₁ + x₂)/2 = 1
x₁ + x₂ = 2
From the third equation: x₁ - x₂ = 10
5. Solving the two equations simultaneously, we can find the values of x₁ and x₂.
Adding the two equations:
x₁ + x₂ + x₁ - x₂ = 2 + 10
2x₁ = 12
x₁ = 6
Subtracting the second equation from the first:
(x₁ + x₂) - (x₁ - x₂) = 2 - 10
2x₂ = -8
x₂ = -4
6. Now that we have the values of x₁ and x₂, we can substitute them back into any of the original equations to find the value of y.
Using the first equation: (x₁ + x₂)/2 = 1
(6 + (-4))/2 = 1
2/2 = 1
1 = 1
So, we found that the value of y is 1.
7. Therefore, the coordinates of point A are (6, 1) and the coordinates of point B are (-4, 1).