Distance problem

A=(x, x)
B=(1,4)
Distance AB=√5, find x;

Correct answer:

x₁ =  3
x₂ =  2

Step-by-step explanation:

$$\begin{gathered} (x-1{)}^2+(x-4{)}^2=5 \\ (x-1{)}^2+(x-4{)}^2=5 \\ 2x^2-10x+12=0 \\ a=2;b=-10;c=12 \\ D=b^2-4ac=10^2-4\cdot 2\cdot 12=4 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{10\pm \sqrt{4}}{4}} \\ {x}_{1,2}={\displaystyle \frac{10\pm 2}{4}} \\ {x}_{1,2}=2.5\pm 0.5 \\ {x}_1=3 \\ {x}_2=2 \\ \text{ Factored form of the equation: } \\ 2(x-3)(x-2)=0 \\ {x}_1=3 \end{gathered}$$

Our quadratic equation calculator calculates it.

$x_2=2$

Try another example

Related math problems and questions:

• Distance problem 2
  A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
• On line
  On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
• Equation of circle 2
  Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
• Find the 5
  Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
• Find the 3
  Find the distance and midpoint between A(1,2) and B(5,5).
• Right angled triangle 2
  LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n
• Suppose
  Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
• Distance between 2 points
  Find the distance between the points (7, -9), (-1, -9)
• Prove
  Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
• Parametric form
  Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. ..
• Calculate 6
  Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1].
• Find the 13
  Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4].
• Distance
  Calculate distance between two points X[18; 19] and W[20; 3].
• On a line
  On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
• Sphere equation
  Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
• Vertices of a right triangle
  Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Find parameters
  Find parameters of the circle in the plane - coordinates of center and radius: ?