Subjects geometry

Coordinates Points 17F7Cc

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1. **Problem Statement:** Find the abscissa (x-coordinate) and ordinate (y-coordinate) of points A, B, C, D, and Z on a Cartesian plane. 2. **Understanding Coordinates:** The abscissa of a point is its horizontal distance from the y-axis, and the ordinate is its vertical distance from the x-axis. 3. **Method:** To find the coordinates of a point, draw perpendicular lines from the point to the x-axis and y-axis. The foot of the perpendicular on the x-axis gives the abscissa, and on the y-axis gives the ordinate. 4. **Example:** For point A, if the perpendiculars meet the x-axis at $x=a$ and the y-axis at $y=b$, then coordinates of A are $(a,b)$. 5. **Equation of Line Segments:** To find the equation of line segments like $\overline{MA}$, $\overline{CE}$, $\overline{XW}$, and $\overline{YZ}$, use the two-point form of a line equation: $$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$$ where $(x_1,y_1)$ and $(x_2,y_2)$ are coordinates of the endpoints. 6. **Summary:** This method helps locate exact positions on a map or graph by identifying coordinates and equations of lines connecting points. Final answer: Coordinates of points A, B, C, D, Z can be found by dropping perpendiculars to axes; line equations use two-point formula.