Question

In what ratio is the line segment joining (–3, 1) and (7, –2) divided by the line 2x – y = 7?

Answer 1

Answer:

14 : 9 ratio

Step-by-step explanation:

line segment joining (–3, 1) and (7, –2)

slope = (-2 - 1)/(7 -(-3))

= - 3/10

y = (-3/10)x + c

1 = (-3/10)(-3) + c

=> 1 = 9/10 + c

=> c = 1/10

y = (-3/10)x + 1/10

=> 10y  =  - 3x + 1

=> 3x + 10y = 1    Eq1

intersect  the line 2x – y = 7     Eq1

2 * Eq1 - 3 * Eq2

=> 20y + 3y = 2 - 21

=> 23y = -19

=> y = -19/23

2x + 19/23 = 7

=> 2x =  142/23

=> x = 71/23

now 71/23 ,  -19/23

divided the (–3, 1) and (7, –2)  in m : n ration

=>  71/23  =  (7m - 3n)/(m + n)

&  -19/23 = (-2m +  n)/(m + n)

71m + 71 n = 161m - 69n

=> 140n = 90m

=> m /n = 14/9

or

-19m - 19n = -46m + 23n

=> 27m = 42n

=> m/n = 14/9

line segment joining (–3, 1) and (7, –2) divided by the line 2x – y = 7

in 14 : 9 ratio