How To Solve: Co-ordinate Geometry Basics

How To Solve: Co-ordinate Geometry Basics

Attached pdf of this Article as SPOILER at the top! Happy learning!

Hi All,

I have recently uploaded a video on YouTube to discuss Co-ordinate Geometry Basics in Detail:




Following is covered in the video

¤ XY or 2D Plane
¤ Introduction to Quadrants
¤ x-intercept and y-intercept
¤ Distance between two points
¤ Distance of a point from origin
¤ Slope of a line
¤ Sign of slope of a line
¤ Slope of Parallel and Perpendicular lines

XY or 2D Plane

XY Plane is a 2D Plane which contains the x-axis and the y-axis. x-axis is horizontal axis and y-axis is vertical axis.

¤ Each point in the XY Plane has two co-ordinates (x,y)
¤ x is the x co-ordinate, y is the y co-ordinate




Introduction to Quadrants

x-axis and y-axis divide the XY plane into 4 quadrants.

¤ \(1^{st}\) Quadrant : x +ve, y +ve
¤ \(2^{nd}\) Quadrant : x -ve, y +ve
¤ \(3^{rd}\) Quadrant : x -ve, y -ve
¤ \(4^{th}\) Quadrant : x +ve, y -ve




x-intercept and y-intercept

x-intercept : Point where a line touches the x-axis
y-intercept : Point where a line touches the y-axis




Distance between two points

Distance, d, between two points A (x1,y1) and B(x2,y2) on a XY plane is given by

d = \(\sqrt{((𝒙_𝟐 − 𝒙_𝟏)^𝟐 + (𝒚_𝟐 − 𝒚_𝟏)^𝟐)}\)




Distance of a point from Origin

Distance, d, of a point A (a,b) from origin (0,0) is given by

d = \(\sqrt{((a − 0)^𝟐 + (b − 0)^𝟐)}\) = \(\sqrt{a^𝟐 + b^𝟐}\)




Slope of a Line

Slope of a line is an indication of how inclined the line is as compared to positive x-axis.

¤ Slope(m) of line(l) passing through points A and B is given by
m = \(\frac{(𝒚_𝟐 − 𝒚_𝟏)}{(𝒙_𝟐 − 𝒙_𝟏)}\)




Sign of slope of a line

¤ Positive Slope: Line tilted towards right
¤ Negative Slope: Line tilted towards left
¤ Zero Slope: Line parallel to x-axis
¤ Infinite Slope: Line parallel to y-axis




Slope of Parallel and Perpendicular Lines

If two lines are Parallel, then their slopes will be equal.

¤ If we have two parallel lines \(L_1\) and \(L_2\), with below equations
¤ Line L1 : y = \(m_1\)x + \(c_1\)
¤ Line L2 : y = \(m_2\)x + \(c_2\)
¤ then \(m_1\) = \(m_2\)



If two lines are Perpendicular, then product of their slopes will be equal to -1

¤ If we have two perpendicular lines \(L_1\) and \(L_2\), with below equations
¤ Line L1 : y = \(m_1\)x + \(c_1\)
¤ Line L2 : y = \(m_2\)x + \(c_2\)
¤ then \(m_1\) * \(m_2\) = -1




Link to next post on Equation of a Line is here

Watch the following video to learn about Equation of a Line



Hope it helps!
Good Luck!
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