Learn Class 10 Math - Coordinate Geometry

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The term coordinate geometry refers to getting the solution with the help of algebraic methods. The major formula is present for the distance between two points that we have to use. The formula consists of x and y terms.

Formula:

  • The formula for the coordinate geometry is represented by x and y.
  • The formula is √(x2 - x1)^2 + (y2 - y1)^2
  • The formula is also called the distance formula.
  • The midpoint formula for the coordinate geometry is represented by x1, y1, and x2, y2.
  • The slope of line is represented by m ,i.e. m = -a / b.

Triangle centroid:

  • The centroid of the triangle is the point where the triangle's median intersection point is present.

Components of Coordinate geometry:

  • Circle

    The circle is a defined set of all points within a coordinate plane. And it is equidistant from the plane's fixed points.

  • Parabola

    It is the complete set of all the given points in a plane. And the sum of those points will remain constant.

  • Hyperbola

    Hyperbola is when all the difference of the terms from the fixed plane remains constant.

  • The inclination of a line

    The line inclination is from the points that make the constant angles with the x-axis.

Learning Videos for 10th Grade Math - Coordinate Geometry

Coordinate Geometry Sample Questions for Class 10

Question 1

Let f(x) be the function in the graph below. Assume that the horizontal axis represents x values and the vertical axis y values. What is the value of f^{-1}(2) ?
A. -2
B. 1
C. 2
D. 4

Question 2

Where is the output of the function graphed below less than 2? Assume the horizontal axis represents x and the vertical axis represents y.
A. x<2
B. -2 < y < 2
C. -2 < x < 2
D. y<2

Question 3

((x_1+x_2)/2),((y_1+y_2)/2)
A. Midsegment
B. Sides + Diagonals
C. Distance Formula
D. Equation of a Circle

Question 4

Point A'(12,4) is the image of point A(3,1) under a dilation with respect to the origin. What is the constant of dilation?
A. 9
B. 1/4
C. 3
D. 4

Question 5

Given two linear functions, f(x) which has some of its values listed in the table and g(x) represented graphically, determine which function has a greater slope. If the slopes are equal, determine whether the lines are coincident or not. Let m_f represent the slope of function f and m_g represent the slope of function g. \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ -2 7 -1 4 0 1 1 -2 2 -5
A. m_f > m_g
B. m_f < m_g
C. m_f = m_g The lines are not coincident.
D. m_f = m_g The lines are coincident.

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