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AP SSC Class 10 Maths Chapter 7 Coordinate Geometry

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
    \(\begin{array}{l}A(x_{1},y_{1})\end{array} \)
    and
    \(\begin{array}{l}B(x_{2},y_{2})\end{array} \)
    is calculated using the formula
    \(\begin{array}{l}\sqrt{(x_{2}-x_1)^{2}+(y_{2}-y_1)^2}\end{array} \)
  • The distance between a pointP(x,y) and the origin is given by
    \(\begin{array}{l}\sqrt{x^2+y^2}\end{array} \)
  • Distance between two points
    \(\begin{array}{l}x_{1},y_{1}\end{array} \)
    and
    \(\begin{array}{l}x_{2},y_{2}\end{array} \)
    on line parallel to Y-axis is
    \(\begin{array}{l}\left | y_{2}-y_{1} \right |\end{array} \)
    .
  • Distance between two points
    \(\begin{array}{l}x_{1},y_{1}\end{array} \)
    and
    \(\begin{array}{l}x_{2},y_{2}\end{array} \)
    on line parallel to X-axis is
    \(\begin{array}{l}\left | x_{2}-x_{1} \right |\end{array} \)
    .
  • The coordinates of the point P(x, y) which divides the line segment joining the points A
    \(\begin{array}{l}x_{1},y_{1}\end{array} \)
    and B
    \(\begin{array}{l}x_{2},y_{2}\end{array} \)
    ) internally in the ratio
    \(\begin{array}{l}m_{1}:m_{2}\end{array} \)
    are
    \(\begin{array}{l}\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}},\end{array} \)
  • The mid-point of the line segment joining the points P
    \(\begin{array}{l}x_{1},y_{1}\end{array} \)
    and
    \(\begin{array}{l}x_{2},y_{2}\end{array} \)
    is given by
    \(\begin{array}{l}(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\end{array} \)
  • The Heron’s formula or the area of the triangle is given as
    \(\begin{array}{l}A=\sqrt{S(S-a)(S-b)(S-c))}\end{array} \)
    where
    \(\begin{array}{l}S=\frac{a+b+c}{2}\end{array} \)
    .
  • A slope of a line is determined as follows
    \(\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\end{array} \)

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

    1. 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 =

\(\begin{array}{l}\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2}\end{array} \)

Substituting the values in the equation, we get

D =

\(\begin{array}{l}\sqrt{(36-0)^2+(15-0)^2}\end{array} \)

D =

\(\begin{array}{l}\sqrt{1296+225}\end{array} \)

D =

\(\begin{array}{l}\sqrt{1521}\end{array} \)

D = 39

The distance between two points is 39.

    1. 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

\(\begin{array}{l}x_{1},y_{1}\end{array} \)
and
\(\begin{array}{l}x_{2},y_{2}\end{array} \)
is given by
\(\begin{array}{l}(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\end{array} \)

Substituting the values in the formula, we get

\(\begin{array}{l}M(x,y)=(\frac{5+(-3)}{2},\frac{0+6}{2})\end{array} \)
\(\begin{array}{l}M(x,y)= (\frac{2}{2},\frac{6}{2})\end{array} \)
\(\begin{array}{l}M(x,y)= (1,3)\end{array} \)

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