Important Straight Line Formulas For JEE

# Important Straight Line Formulas For JEE

## Formulas for the straight line

1. Distance formula:

d = √[(x2-x1)2+(y2-y1)2]

2. Section Formula:

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x = (mx2+nx1)/(m+n)

y = (my2+ny1)/(m+n)

3. Centroid:

G = [(x1+x2+x3)/3, (y1+y2+y3)/3]

4. Incentre:

I = {(ax1+bx2+cx3)/(a+b+c), (ay1+by2+cy3) / (a+b+c)}

5. Excentre:

I1 = {(-ax1+bx2+cx3)/(-a+b+c), (-ay1+by2+cy3)/(-a+b+c)}

6. Slope formula:

(i) Line joining two points (x1, y1) and (x2, y2), m = (y1 – y2) / (x1 – x2)

(ii) Slope of a line ax+by+c = 0 is -coefficient of x/coefficient of y = -a/b

7. Equation of a straight line in various forms:

(i) Point Slope form: y-y1 = m(x – x1)

(ii) Slope intercept form: y = mx + c

(iii) Two point form: y-y1 = {(y2 – y1) / (x2 – x1)} × (x-x1)

(iv) Intercept form: (x/a) + (y/b) = 1

(v) Perpendicular / Normal form: x cos α +y sin α = p

(vi) Parametric form: x = x1+ r cos θ , y = y1 + r sin θ

(vii) Symmetric form: (x – x1)/cos θ = (y – y1) / sin θ = r

(viii) General form: ax + by + c = 0

x intercept = -c/a

y intercept = -c/b

8. Parallel lines:

Two lines ax+by+c = 0 and a’x+b’y+c’ = 0 are parallel if a/a’ = b/b’ ≠ c/c’.

Thus any line parallel to ax+by+c = 0 is of the type ax+by+k = 0, where k is a parameter.

9. Perpendicular lines:

Two lines ax+by+c = 0 and a’x+b’y+c’ = 0 are perpendicular if aa’+bb’ = 0

10. Position of the points (x1, y1) and (x2, y2) relative to the line ax+by+c = 0:

In general, two points (x1, y1) and (x2, y2) will lie on the same side or opposite side of ax+by+c = 0 according to ax1+by1+c and ax2+by2+c are of the same or opposite sign respectively.

11. Length of the perpendicular from a point on a line :

The length of the perpendicular from a point (x1, y1) to a line ax + by + c = 0 is

12. Reflection of a point about a line:

(i) Foot of the perpendicular from a point on the line is (x-x1)/a = (y-y1)/b = -(ax1+by1+c)/(a2+b2)

(ii)Image of (x1, y1) in the line ax+by+c = 0 is (x-x1)/a = (y-y1)/b = -2 (ax1+by1+c)/(a2+b2)

## FAQs:

##### Is straight line significant for JEE?

Yes, it is still in JEE prospectus. It is one of the significant subjects of Coordinate Geometry, so don't miss it.

##### Are recipes significant for JEE?

The JEE Main significant recipes can help applicants in different ways: It helps in saving time for the test. Makes the estimations simpler. Decreases the gamble of errors.

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