Subjects geometry

Boundary Lines Aebc85

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem Statement:** Define the four boundary lines of a recreational park given its coordinates and label them on a coordinate grid. 2. **Understanding Boundary Lines:** Boundary lines of a park are straight lines connecting the given corner points (coordinates) of the park. Each line can be represented by a linear equation in the form $y=mx+b$ or $Ax+By=C$. 3. **Step-by-step Approach:** - Identify the four corner points of the park (assumed given or to be provided). - For each pair of adjacent points, calculate the slope $m=\frac{y_2-y_1}{x_2-x_1}$. - Use point-slope form $y-y_1=m(x-x_1)$ to find the equation of each boundary line. - Simplify each equation to slope-intercept form $y=mx+b$ or standard form. 4. **Example:** Suppose the park corners are $A(1,2)$, $B(5,2)$, $C(5,6)$, and $D(1,6)$. - Line AB: slope $m=\frac{2-2}{5-1}=0$, equation $y=2$. - Line BC: slope $m=\frac{6-2}{5-5}=\infty$, vertical line $x=5$. - Line CD: slope $m=\frac{6-6}{1-5}=0$, equation $y=6$. - Line DA: slope $m=\frac{2-6}{1-1}=\infty$, vertical line $x=1$. 5. **Labeling:** On the coordinate grid, draw and label lines AB, BC, CD, and DA accordingly. This method applies to any four points forming a recreational park boundary.