Coordinate geometry is one of the widely used topics of mathematics. It is one of those topics which is a necessity for every student who wants to pursue a career in engineering. Coordinate geometry has a wide variety of topics to study. Coordinate geometry is one of those topics of mathematics that has been taught to students of higher secondary standards. Some of the basic topics and formulas which are taught to students are distance formula, midpoint formula, and many other basic formulas which are widely used in coordinate geometry. There are various curves too which students study in coordinate geometry. Curves like ellipse, parabola, and hyperbola are studied by students.
This article discusses coordinate geometry and different types of formulas that are used in basic coordinate geometry.
Listed below are some of the formulas and terms which are widely used in Co-ordinate geometry:
- The slope of the line: It is measured as the inclination which is made by the line with the axis. The angle of inclination is theta then the slope of the line in terms of theta is defined as tan theta. In terms of coordinate, it can be defined as the difference in y coordinate upon x-coordinates of the given line.
- Midpoint formula: This formula is used in taking out the value of the midpoint of the given line with help of coordinates. The point which is located absolutely middle of the line is termed as the midpoint. It can be found out by adding up the extremes of the x coordinate of the line and dividing it by two, this will give the x coordinate of the midpoint of the line. To find out the y co-ordinate one has to perform the same steps. This will help in finding both the co-ordinate of the line.
- Distance formula: This formula is used in finding out the distance between two points that lie in the same or different coordinate planes. It can be found out by the sum of the square of the difference between the x-coordinates and y- coordinate the complete equation should be taken under the square root.
- Section formula: The section formula is used in finding out the exact coordinate of the point that divides the line segment joining the coordinate in the ratio of m:n. The point can then divide the line segment internally or externally. The value of this can be found out with the help of the section formula.
- The centroid of the triangle: The point inside the triangle where all the medians of the triangle meet are termed as a centroid. First of all, let’s discuss the median, it can line which joins the vertex of the triangle with the mid-point which lies on the opposite side. The x and the y coordinate of the centroid can be found out by adding up the respective co-ordinate of the triangle and dividing them by three.
Listed below are some of the tips and tricks to master coordinate geometry:
- One always needs to remember that the slope of the x-axis is zero and the slope of the y-axis is infinity.
- A point which is on the x-axis has the value as (x,0) whereas the point on the y axis has the value of its co-ordinate as the (0,y).
- The lines which will never meet each other are known as parallel lines. If two lines are parallel to each then the value of their slopes are equal to each other.
- The line which is at ninety degrees to each other is known as the perpendicular lines. The product of slopes of two lines that are perpendicular to each other has a value that is equal to -1.
- One needs to by heart all the slope forms of the lines that are a point-slope form of line and intercept form too.
These were some tips to keep in mind while solving coordinate geometry. If any kind of doubt arises in the mind of students related to co-ordinate geometry or mathematics, then one can make a google search of Cuemath, this website will help in clearing all the doubt of the student.