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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
ยค XY or 2D Plane ยค Introduction to Quadrants ยค x-intercept and y-intercept ยค Distance between two points ยค Distance of a point from origin ยค Slope of a line ยค Sign of slope of a line ยค 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.
ยค Each point in the XY Plane has two co-ordinates (x,y) ยค x is the x co-ordinate, y is the y co-ordinate
Attachment:
xy plane.jpg [ 13.63 KiB | Viewed 1365 times ]
Introduction to Quadrants
x-axis and y-axis divide the XY plane into 4 quadrants.
ยค 1st Quadrant : x +ve, y +ve ยค 2nd Quadrant : x -ve, y +ve ยค 3rd Quadrant : x -ve, y -ve ยค 4th Quadrant : x +ve, y -ve
Attachment:
Quadrants.jpg [ 31.7 KiB | Viewed 1383 times ]
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
Attachment:
Intercepts.jpg [ 19.33 KiB | Viewed 1359 times ]
Distance between two points
Distance, d, between two points A (x1,y1) and B(x2,y2) on a XY plane is given by
d = โ((๐๐โ๐๐)๐+(๐๐โ๐๐)๐)
Attachment:
Distance between points.jpg [ 18.78 KiB | Viewed 1367 times ]
Distance of a point from Origin
Distance, d, of a point A (a,b) from origin (0,0) is given by
d = โ((aโ0)๐+(bโ0)๐) = โa๐+b๐
Attachment:
Distance from origin.jpg [ 17.25 KiB | Viewed 1334 times ]
Slope of a Line
Slope of a line is an indication of how inclined the line is as compared to positive x-axis.
ยค Slope(m) of line(l) passing through points A and B is given by m = (๐๐โ๐๐)(๐๐โ๐๐)
Attachment:
Slope of a line.jpg [ 18.51 KiB | Viewed 1370 times ]
Sign of slope of a line
ยค Positive Slope: Line tilted towards right ยค Negative Slope: Line tilted towards left ยค Zero Slope: Line parallel to x-axis ยค Infinite Slope: Line parallel to y-axis
Attachment:
Sign of slope.jpg [ 22.08 KiB | Viewed 1382 times ]
Slope of Parallel and Perpendicular Lines
If two lines are Parallel, then their slopes will be equal.
ยค If we have two parallel lines L1 and L2, with below equations ยค Line L1 : y = m1x + c1 ยค Line L2 : y = m2x + c2 ยค then m1 = m2
Attachment:
Parallel Lines.jpg [ 4.93 KiB | Viewed 1360 times ]
If two lines are Perpendicular, then product of their slopes will be equal to -1
ยค If we have two perpendicular lines L1 and L2, with below equations ยค Line L1 : y = m1x + c1 ยค Line L2 : y = m2x + c2 ยค then m1 * m2 = -1
Attachment:
Perpendicular Lines.jpg [ 3.41 KiB | Viewed 1366 times ]