Advertisements
Advertisements
Question
Calculate the ratio in which the line joining A(−4, 2) and B(3, 6) is divided by point P(x, 3). Also, find
- x
- length of AP.
Solution
Given points are A(–4, 2) and B(3, 6)
Let P(x, 3) divides the line joining A(4, 2) and B(3, 6) in the ratio k : 1.
Thus, we have
`(3k - 4)/(k +1) = x` ...(i)
And `(6k + 2)/(k +1) = 3`
6k + 2 = 3(k + 1)
`=>` 6k + 2 = 3k + 3
`=>` 3k = 1
`=> k= 1/3`
Substituting the value of k in equation (i), we have
i. `(3 xx 1/3 -4)/(1/3 + 1) = x`
`=> (-3)/(4/3) = x`
`=> (-9)/4 = x`
Therefore, coordinates of P are `(-9/4 , 3)`
ii. Now let us find the distance AP
`AP = sqrt((-9/4 +4)^2 + (3 - 2)^2)`
= `sqrt((7/4)^2 + (1)^2)`
= `sqrt(49/16 + 1)`
= `sqrt((49 + 16)/16)`
= `sqrt(65/16)`
`=> AP = sqrt(65)/4` units
APPEARS IN
RELATED QUESTIONS
Find the value of x, if: (2x + 1) : (3x + 13) is the sub-duplicate ratio of 9 : 25.
There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3 : 1. How any more girls should be added to the council so that the ratio of the number of boys to the number of girls may be 9 : 5?
Convert the following percentage to fractions and ratio:
125%
Check whether the following quantities form a proportion or not?
`1 1/2, 3 1/4, 4 1/2 "and" 9 3/4`
Find the fourth term of the proportion whose first, second, and third terms are 18, 27, and 32 respectively.
The ratio between 7 and 5 is same as the ratio between ₹ x and ₹ 20.50; find the value of x.
Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.
The ratio of the pocket money saved by Lokesh and his sister is 5 : 6. If the sister saves Rs 30 more, how much more the brother should save in order to keep the ratio of their savings unchanged?
Present age of father is 42 years and that of his son is 14 years. Find the ratio of present age of father to the present age of son.
