Solve {l}{x1=72}{y1=298}{x2=76}{y2=767}{d=sqrt{(x2-x1)^2+(y2-y1)^2}}

$$\left. \begin{array} { l } { x 1 = 72 } \\ { y 1 = 298 } \\ { x 2 = 76 } \\ { y 2 = 767 } \\ { d = \sqrt { ( x 2 - x 1 ) ^ { 2 } + ( y 2 - y 1 ) ^ { 2 } } } \end{array} \right.$$

Solve for x_1, y_1, x_2, y_2, d

$$x_{1}=72$$

$$y_{1}=298$$

$$x_{2}=76$$

$$y_{2}=767$$

$$d=\sqrt{219977}\approx 469.017057259$$

Solution Steps

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

$$d=\sqrt{\left(76-72\right)^{2}+\left(767-298\right)^{2}}$$

Subtract 72 from 76 to get 4.

$$d=\sqrt{4^{2}+\left(767-298\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$d=\sqrt{16+\left(767-298\right)^{2}}$$

Subtract 298 from 767 to get 469.

$$d=\sqrt{16+469^{2}}$$

Calculate 469 to the power of 2 and get 219961.

$$d=\sqrt{16+219961}$$

Add 16 and 219961 to get 219977.

$$d=\sqrt{219977}$$

The system is now solved.

$$x_{1}=72 y_{1}=298 x_{2}=76 y_{2}=767 d=\sqrt{219977}$$