Solve {l}{x_{1}=-2}{x_{2}=1}{y_{1}=2}{y_{2}=-2}{a=sqrt{{(x_{2}-x_{1})}^2+{(y_{2}-y_{1})}^2}}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { x_{1} = -2 }\\ { x_{2} = 1 }\\ { y_{1} = 2 }\\ { y_{2} = -2 }\\ { a = \sqrt{{(x_{2} - x_{1})} ^ {2} + {(y_{2} - y_{1})} ^ {2}} }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x_1, x_2, y_1, y_2, a, b

$$b=5$$

Solution Steps

Consider the fifth equation. Insert the known values of variables into the equation.

$$a=\sqrt{\left(1-\left(-2\right)\right)^{2}+\left(-2-2\right)^{2}}$$

Multiply -1 and -2 to get 2.

$$a=\sqrt{\left(1+2\right)^{2}+\left(-2-2\right)^{2}}$$

Add 1 and 2 to get 3.

$$a=\sqrt{3^{2}+\left(-2-2\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$a=\sqrt{9+\left(-2-2\right)^{2}}$$

Subtract 2 from -2 to get -4.

$$a=\sqrt{9+\left(-4\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$a=\sqrt{9+16}$$

Add 9 and 16 to get 25.

$$a=\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$a=5$$

Consider the equation (6). Insert the known values of variables into the equation.

$$b=5$$

The system is now solved.

$$x_{1}=-2 x_{2}=1 y_{1}=2 y_{2}=-2 a=5 b=5$$