Co-Ordinates
👉 Distance Formula
🔹 The distance between two points
🔹 Distance from the origin
Solve the problems below with the Distance Formula.
🔹 Find the distance between the points (3, -5) and (5, -1)
🔹 If the distance between the points (a, -2) and (0, 0) is √29 unit, find the value(s) of a.
🔹 Shoe that, the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right angled triangle
🔹 Two vertices of an isosceles triangle are (2, 0) and (2, 5), Find the third vertex if the equal length of sides is 3 units.
🔹 Show that, the distance between two points and is not depend on the value of .
👉 Section Formula
🔹 Section Formula for Internal Division
Point P internally divides points A and B
with m : n ratio
🔹 Section Formula for External Division
Point P externally divides points A and B
with m : n ratio
🔹 Section Formula for Mid-point
Point P is the midpoint of points A and B
as AP : PB = 1 : 1 ratio
Solve the problems below with the Section Formula.
🔹 Find the coordinates of the point which divides the join of the points (8, 9) and (–7, 4) internally in the ratio 2 : 3.
🔹 In what ratio is the line joining the points A(4, 4) and B(7, 7) divided by P(–1, –1)?
🔹 Find the ratio in which the x-axes divides the line joining the points (–2, 5) and (1, –9) ?
🔹 Find the point of trisection of the line segment joining the points (1, 2) and (11, 9) ?
👉 Some Important Points Relating to a Triangle:
🔹 Centroid of a triangle
the point where the three medians intersect, which is also its geometric center or center of mass.
as AG : GL = 2 : 1 ratio
🔹 Incenter of a Triangle
The point where the three angle bisectors intersect.
The incenter using the vertices' coordinates and opposite side lengths
🔹 Circumcentre of a Triangle
The Point of concurrence of perpendicular bisectors.
This point is equidistant from all three vertices OA=OB=OC and is the center of the circumscribed circle that passes through the vertices. The coordinates can be found by solving simultaneous linear equations derived from the distance formula.
👉 Area of a triangle with given vertices :
the vertices are A(x1, y1), B(x2, y2) and C(x3, y3)
🔹 Area of a triangle
🔹 Condition of collinearity of three points
If three points be on a straight line, the area of the triangle by them is zero