Equations of line Flashcards
What is rectangular Coordinate system?
X and Y axis is called a coordinate plane. Since X and Y axis are intersecting at right angles, we call them rectangular coordinate system. The point of intersection of X and Y axis is called origin. Any point on the coordinate plane can be represented by an ordered pair (x, y) . Has 4 quardrants.
Quadrant 1 ( X and Y are positive)
Quadrant 2 (X is negative Y is positive)
Quadrant 3 (X is negative Y is negative)
Quadrant 5 (X is positive Y is negative)
Distance of a point from origin?
Distance of point P (x,y) from Origin O (0,0) is sqrt (x^2+y^2)
Distance between any two point?
Distance between point P( x1, y1) and Q(x2,y2) then distance between them is sqrt((x2-x1)^2 -(y2-y1)^2)
What is section formula?
Given point P which cuts line segment AB in ration m:n , if our goal is to find the coordinates of P then the answer is
x= (mx2+nx1)/(m+n)
y=(my2+ny1)/(m+n)
What is the area of triangles using coordinates?
If there are three points A (x1,y1) , B(x2,y2), C (x3,y3) are point of triangle (in anti clockwise direction) then area of triangle ABC is 1/2 *abs(x1(y2-y3) +x2(y3-y1)+x3(y1-y2))
How to find slope of a line ?
2 points in the coordinate plane is enough to determine slope of the line.
slope of the line = (change in y direction / change in x direction ) aka gradient of line (l). Slope can be positive, negative or zero.
slope = (y2-y1) / (x2-x1)= tanɵ
where ɵ is the inclination of the line with positive x-axis measured in anticlockwise direction. (0<= ɵ <=180). Note if ɵ=0 it means horizontal line (slope is 0) if ɵ=90 (vertical line, slope is undefined)
given a slope, can we find out the line?
No. Slope can be same for many lines so there are infinitely many answers.
How is slope useful?
Slope for parallel lines is same. (used for proving two lines are parallel)
product of slope of perpendicular lines is -1
What is the angle of intersection of two lines?
tanɵ = (m2-m1/(1+m1m2), given m1m2!=-1where ɵ is angle between lines in x direction
tanФ = tan(180 - ɵ) = (m1-m2)/(1+m1m2), given m1m2!=-1 where Ф is angle between lines in y direction.
Representation of line?
y=mx+c (slope intercept form)
(y- y0)=m(x-x0) - point slope form
(y-y1)/(x-x1) = (y2-y1)/(x2-x1) - Two point form
x/a + y/b =1 where x intercept is (a,0) and y intercept is (0,b)
General Form - Ax +By+C =0 , aka general linear equation or general equation of a line
how to find distance of a point from a line?
let P (x,y) be a point and line l is having equation Ax+By+C=0 then x-intercept = -C/A , y-intercept is -C /B. distance between point P and line L = |Ax1+By1+c| / sqrt(A^2+B^2)
How to find distance between 2 parallel lines?
d = |C1-C2|/ sqrt(A^2+B^2)
What is straight line fit?
when there are many points , we need to draw a line that best respresents the points and has minimal squared standard error. such a line is called line of best fit.
What is squared standard error?
If (xi,yi) are many points and line y=mx+c then
SSE = summation from i=1 to n (yi-mxi-c)^2.
we need to find the values of m and c which makes the above equation to a minimum value and thats the line of best fit.
