Question

Coordinate geometry all formulas
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Answer 1

Answer:

Pythagorean theorem to find the length of the hypotenuse gives the distance formula. The distance between the two points in a triangle is called the hypotenuse.

The distance formula can also be used to calculate the lengths of all the sides of a polygon, the perimeter of polygons on a coordinate plane, the area of polygons, and several other things.

The distance formula is denoted by ‘d’.

Distance Formula Between 2 Points in a 2D Plane:

Consider 2 points P and Q having the 2D coordinates as (x1,y1) and (x2,y2) respectively.

Now the distance between these 2 points in the 2D plane is

d=PQ=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

Distance Formula Between 2 Points in a 2D Plane in Polar Coordinates:

Consider 2 points P and Q having the 2D polar coordinates as (r1,θ1) and (r2,θ2) respectively.

Now the distance between these 2 points in the 2D plane is

d=PQ=r21+r22−2r1r2cos(θ1−θ2)−−−−−−−−−−−−−−−−−−−−−√

Distance Formula Between 2 Points in a 3D Plane:

Consider 2 points P and Q having the 3D coordinates as (x1,y1,z1) and (x2,y2,z2) respectively.

Now the distance between these 2 points in the 3D plane is

d=PQ=(x2−x1)2+(y2−y1)2+(z2−z1)2−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

Distance Formula Between a Point and a Line

Consider a straight line Ax + By + C = 0 and point P having the 2D coorrdinates as (x1, y1).

Now the distance between the line Ax + By + C = 0 and a point P (x1, y1) is

d=|Ax+By+C|A2+B2−−−−−−−√

Distance Formula Between Two Parallel Points

Consider two parallel lines y = mx + c1 and y = mx + c2.

Now the distance between these two parallel lines is given by

d=|c1−c2|A2+B2−−−−−−−√

Problems on Distance formula

1. Find the distance between two points A and B which are having the 2D coordinates as (4, 8) and (3, 6) respectively.

Ans: The distance between these 2 points in the 2D plane is

d=AB=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

Here x1 = 4, x2 = 8, y1 = 3 and y2 = 6. Now substituting these values in the distance formula we get,

d=AB=(8−4)2+(6−3)2−−−−−−−−−−−−−−−√

d=AB=(4)2+(3)2−−−−−−−−−√

d=AB=16+9−−−−−√

d=AB=25−−√

d = AB = 5 units

So the distance between 2 points A and B is 5 units.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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