Question

Помогите пожалуйста на координатной прямой выбраны точки А(2х+1) и В(х).определите,при каких значениях х длина отрезка АВ равна 2? С подробным решением !!! Срочно!!!

Answer 1

AB=|X-2X-1|=|-X-1|=2

X=1

X=-3

Answer 2

Solving for the Length of Line Segment AB

To determine the values of x for which the length of the line segment AB is equal to 2, we can use the distance formula. The distance formula between two points A(x1, y1) and B(x2, y2) in a coordinate plane is given by:

Distance Formula: The distance, d, between points A(x1, y1) and B(x2, y2) is given by: \[ d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \]

Applying the Distance Formula to Points A and B

Given that point A is (2x + 1) and point B is (x), we can use the distance formula to find the values of x for which the length of the line segment AB is equal to 2.

The distance formula for the line segment AB is: \[ d = \sqrt{(x - (2x + 1))^2 + (y - y)^2} \]

Simplifying the Distance Formula

Simplifying the distance formula for the line segment AB gives: \[ d = \sqrt{((-x - 1)^2 + (0)^2)} \] \[ d = \sqrt{(x^2 + 2x + 1)} \]

Setting the Length of AB to 2

To find the values of x for which the length of the line segment AB is equal to 2, we set the distance d equal to 2 and solve for x: \[ 2 = \sqrt{(x^2 + 2x + 1)} \]

Solving for x

Squaring both sides of the equation gives: \[ 4 = x^2 + 2x + 1 \] \[ 0 = x^2 + 2x - 3 \]

Using the quadratic formula, we can solve for x: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Where a = 1, b = 2, and c = -3.

Calculating the Values of x

Using the quadratic formula, we find: \[ x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-3)}}{2(1)} \] \[ x = \frac{-2 \pm \sqrt{4 + 12}}{2} \] \[ x = \frac{-2 \pm \sqrt{16}}{2} \] \[ x = \frac{-2 \pm 4}{2} \]

This gives us two possible values for x: \[ x_1 = \frac{-2 + 4}{2} = 1 \] \[ x_2 = \frac{-2 - 4}{2} = -3 \]

Conclusion

Therefore, the values of x for which the length of the line segment AB is equal to 2 are x = 1 and x = -3.