In what ratio is the line segment joining the points 3/5 and 4 2 divided by Y axis?

(i) Calculate the ratio in which the line segment joining (3, 4) and( – 2, 1) is divided by the y-axis. (ii) In what ratio does the line x – y – 2 = 0 divide the line segment joining the points (3, – 1) and (8, 9)? Also, find the coordinates of the point of division.

Solution:

(i) Let m:n be the ratio in which the line segment joining (3,4) and (-2,1) is divided by the Y axis.

Since the line meets Y axis, its x co-ordinate is zero.

Here x1 = 3, y1 = 4

x2 = -2, y2 = 1

By section formula, x = (mx2+nx1)/(m+n)

0 = (m×-2+n×3)/(m+n)

0 = (-2m+3n)/( m+n)

0 = -2m+3n

2m = 3n

m/n = 3/2

Hence the ration m:n is 3:2.

(ii)Let the line x-y-2 = 0 divide the line segment joining the points (3,-1) and (8,9) in the ratio m:n at the point P(x,y)

Here x1 = 3, y1 = -1

x2 = 8 y2 = 9

By section formula, x = (mx2+nx1)/(m+n)

x = (m×8+n×3)/(m+n)

x = (8m+3n)/( m+n) …. (i)

By Section formula y = (my2+ny1)/(m+n)

y = (m×9+n×-1)/(m+n)

y = (9m-n)/(m+n) …. (ii)

Since the point P(x,y) lies on the line x-y-2 = 0,

eqn (i) and (ii) will satify the equation x-y-2 = 0 …(iii)

Substitute (i) and (ii) in (iii)

[(8m+3n)/( m+n)] – [(9m-n)/(m+n)]-2 = 0

[(8m+3n)/( m+n)] – [(9m-n)/(m+n)]-[2(m+n)/(m+n)] = 0

8m+3n-(9m-n)-2(m+n) = 0

8m+3n-9m+n-2m-2n = 0

-3m+2n = 0

-3m = -2n

m/n = -2/-3 = 2/3

Hence the ratio m:n is 2:3.

Substitute m and n in (i)

x = (8m+3n)/( m+n)

x = (8×2+3×3)/(2+3)

x = (16+9)/5

x = 25/5 = 5

Substitute m and n in (ii)

y = (9m-n)/(m+n)

y = (9×2-3)/(2+3)

y = (18-3)/5

y = 15/5 = 3

Hence the co-ordinates of P are (5,3).

The HTET Exam Admit Cards Out 26th November 2022. The exam dates for the HTET 2022 have been postponed. Due to the General Elections, the exam dates for the HTET have been revised. The exam will be conducted on the 3rd and 4th of December 2022 instead of the 12th and 13th of November 2022. The exam is conducted by the Board of School Education, Haryana to shortlist eligible candidates for PGT and TGT posts in Government schools across Haryana. The exam is conducted for 150 marks. The HTET Exam Pattern for Level I, Level II, and Level III exams is different. There will be no negative marking in the exam.