Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Asked by Abhisek | 1 year ago |  67

1 Answer

Solution :-

NCERT Solutions for Class 10 Chapter 7-15

Let P (x1, y1) and Q (x2, y2) are the points of trisection of the

 line segment joining the given points i.e., AP = PQ = QB

Therefore, point P divides AB internally in the ratio 1:2.

x\( \dfrac{(1×(-2) + 2×4)}{3}\)\(\dfrac{(-2 + 8)}{3}\)\( \dfrac{6}{3}\) = 2

y1 = \( \dfrac{ (1×(-3) + 2×(-1))}{(1 + 2)}= \dfrac{ (-3 – 2)}{3}= \dfrac{-5}{3}\)

Therefore: P (x1, y1) = P(2, \( \dfrac{-5}{3}\))

Point Q divides AB internally in the ratio 2:1.

x2 = \( \dfrac{(2×(-2) + 1×4)}{(2 + 1)}= \dfrac{(-4 + 4)}{3}=0\)

y2 = \( \dfrac{(2×(-3) + 1×(-1))}{(2 + 1)}= \dfrac{(-6 – 1)}{3}= \dfrac{-7}{3}\)

The coordinates of the point Q is (0,\( \dfrac{-7}{3}\))

Answered by Pragya Singh | 1 year ago

Related Questions

In the determine whether the given quadratic equations have real roots and if so, And the roots 3x2 – 2x + 2 = 0

Class 10 Maths Coordinate Geometry View Answer

Find the point on x-axis which is equidistant from the points (-2, 5) and (2, -3).

Class 10 Maths Coordinate Geometry View Answer

Answer the following questions:-

(i) Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square. 

(ii) Prove that the points A (2, 3), B (-2, 2), C (-1, -2) and D (3, -1) are the vertices of a square ABCD.

(iii) Name the type of triangle PQR formed by the point \( P(\sqrt{2} , \sqrt{2}), Q(- \sqrt{2}, – \sqrt{2)} and\; R (-\sqrt{6} , \sqrt{6} )\)

Class 10 Maths Coordinate Geometry View Answer

Find a point on the x-axis which is equidistant from the points (7, 6) and (-3, 4).

Class 10 Maths Coordinate Geometry View Answer

Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
 

Class 10 Maths Coordinate Geometry View Answer