AP SSC Class 10 Maths Chapter 7 Coordinate Geometry is worth a mention. Coordinate Geometry is an important branch of mathematics that provides a connection between geometry and algebra in the form of graphs of lines and curves. It helps us locate points on a graph and its applications are spread across fields like dimensional geometry, calculus, etc.
Students preparing for the board exams can refer to this AP SSC 10th Class Maths Chapter 7 Coordinate Geometry notes and solutions to know how to answer the questions and to understand the concepts well.
Important Formulas in Coordinate Geometry
- The distance between two points [latex]A(x_{1},y_{1})[/latex] and [latex]B(x_{2},y_{2})[/latex] is calculated using the formula [latex]\sqrt{(x_{2}-x_1)^{2}+(y_{2}-y_1)^2}[/latex]
- The distance between a pointP(x,y) and the origin is given by [latex]\sqrt{x^2+y^2}[/latex]
- Distance between two points [latex]x_{1},y_{1}[/latex] and [latex]x_{2},y_{2}[/latex] on line parallel to Y-axis is [latex]\left | y_{2}-y_{1} \right |[/latex].
- Distance between two points [latex]x_{1},y_{1}[/latex] and [latex]x_{2},y_{2}[/latex] on line parallel to X-axis is [latex]\left | x_{2}-x_{1} \right |[/latex].
- The coordinates of the point P(x, y) which divides the line segment joining the points A [latex]x_{1},y_{1}[/latex] and B[latex]x_{2},y_{2}[/latex]) internally in the ratio [latex]m_{1}:m_{2}[/latex] are [latex]\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}},[/latex]
- The mid-point of the line segment joining the points P[latex]x_{1},y_{1}[/latex] and [latex]x_{2},y_{2}[/latex] is given by [latex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/latex]
- The Heron’s formula or the area of the triangle is given as [latex]A=\sqrt{S(S-a)(S-b)(S-c))}[/latex] where [latex]S=\frac{a+b+c}{2}[/latex].
- A slope of a line is determined as follows [latex]m=\frac{y_2-y_1}{x_2-x_1}[/latex]
In the next section, let us look at a few solved chapter questions to better understand coordinate geometry.
Class 10 Maths Chapter 7 Coordinate Geometry Solved Questions
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- Find the distance between the points (0, 0) and (36, 15).
Solution:
The distance between two points (0,0) and (36,15) can be calculated using the formula
D = [latex]\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2}[/latex]
Substituting the values in the equation, we get
D = [latex]\sqrt{(36-0)^2+(15-0)^2}[/latex]
D = [latex]\sqrt{1296+225}[/latex]
D = [latex]\sqrt{1521}[/latex]
D = 39
The distance between two points is 39.
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- Find the midpoint of the line segment joining points (5, 0) and (-3, 6).
Solution: The mid-point of the line segment joining the points P[latex]x_{1},y_{1}[/latex] and [latex]x_{2},y_{2}[/latex] is given by [latex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/latex]
Substituting the values in the formula, we get
[latex]M(x,y)=(\frac{5+(-3)}{2},\frac{0+6}{2})[/latex] [latex]M(x,y)= (\frac{2}{2},\frac{6}{2})[/latex] [latex]M(x,y)= (1,3)[/latex]Stay tuned to BYJU’S to get the latest notification on SSC exam along with AP SSC model papers, exam pattern, marking scheme and more.
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