Determine the ratio in which the line 2x + y - 4 = 0 divide the line segment joining the points A(2, -2) and B(3, 7). Also find the coordinates of the point of the division.
Section Formula
50 Likes

Question

Determine the ratio in which the line 2x + y - 4 = 0 divide the line segment joining the points A(2, -2) and B(3, 7). Also find the coordinates of the point of the division.

KnowledgeBoat · Accepted Answer

Let the line 2x + y - 4 divide the line segment AB in the ratio m : n at P. So, by section-formula coordinates of P are, x-coordinate = x = Similarly, y-coordinate = y = Since, P lies on the line 2x + y - 4 = 0. Putting values in Eq 1 for x-coordinate we get, Putting values in Eq 2 for y-coordinate we get, Hence, coordinates of P will be and 2 : 9 is the ratio in which the line 2x + y - 4 divides AB.

Mathematics

Determine the ratio in which the line 2x + y - 4 = 0 divide the line segment joining the points A(2, -2) and B(3, 7). Also find the coordinates of the point of the division.

Section Formula

Related Questions

In what ratio is the line joining the points (4, 2) and (3, -5) divided by the x-axis? Also find the coordinates of the point of division.

If the abscissa of a point P is 2, find the ratio in which it divides the line segment joining the points (-4, 3) and (6, 3). Hence, find the coordinates of P.

ABCD is a parallelogram. If the coordinates of A, B and D are (10, -6), (2, -6) and (4, -2) respectively, find the coordinates of C.

ABCD is a parallelogram whose vertices A and B have coordinates (2, -3) and (-1, -1) respectively. If the diagonals of the parallelogram meet at the point M(1, -4), find the coordinates of C and D. Hence, find the perimeter of the parallelogram.