# 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?

Correct result:

y11 =  26
y12 =  2

#### Solution:

$x_{2}=6 \ \\ y_{2}=14 \ \\ x_{1}=-3 \ \\ \ \\ d=15 \ \\ (x_{1}-x_{2})^2 +(y_{1}-y_{2})^2=d^2 \ \\ (-3-6)^2 +(y_{1}-14)^2=15^2 \ \\ (-3-6)^2 +(y_{1}-14)^2=15^2 \ \\ \ \\ (-3-6)^2 +(q-14)^2=15^2 \ \\ \ \\ q^2 -28q +52=0 \ \\ \ \\ a=1; b=-28; c=52 \ \\ D=b^2 - 4ac=28^2 - 4\cdot 1 \cdot 52=576 \ \\ D>0 \ \\ \ \\ q_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 28 \pm \sqrt{ 576 } }{ 2 } \ \\ q_{1,2}=\dfrac{ 28 \pm 24 }{ 2 } \ \\ q_{1,2}=14 \pm 12 \ \\ q_{1}=26 \ \\ q_{2}=2 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (q -26) (q -2)=0 \ \\ \ \\ y_{11}=q_{1}=26$

Checkout calculation with our calculator of quadratic equations.

${y}_{12}={q}_{2}=2$

We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We thank you!

Showing 1 comment:
Matematik
we make circle k with centre S(x2,y2) and radius r = 15 . Then we make vertical line x= -3 . It make two intersections with circle k thus solutions are two: y11,y12.

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
• Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
• Calculate 8
Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0.
• Square side
Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
• Circle
Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
• 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].
• Equation with abs value
How many solutions has the equation ? in the real numbers?
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
• Circle - AG
Find the coordinates of circle and its diameter if its equation is: ?
• Discriminant
Determine the discriminant of the equation: ?
• Calculation
How much is sum of square root of six and the square root of 225?