Question
The vertices of triangle ABC are A(2, 3), B(8, 5) and
C(5, −1). Find the coordinates of the centroid of the triangle.Solution
Centroid G of triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃): G = ( (x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 ) Here: x₁ = 2, y₁ = 3 x₂ = 8, y₂ = 5 x₃ = 5, y₃ = −1 x-coordinate of centroid = (2 + 8 + 5)/3 = 15/3 = 5 y-coordinate of centroid = (3 + 5 − 1)/3 = 7/3 So centroid is G(5, 7/3).
- Find the sum of all two-digit numbers that are exactly divisible by 7.
Find the smallest 3-digit number which when divided by 6, 8 and 9 leaves the same remainder 3 in each case.
- The ratio of the number of boys to the number of girls who are present in a class is 3:2. The number of girls who are absent is 15, which is 25% of the tot...
A number when divided by 315 leaves remainder 46 and the value of quotient is 7. Find the number.
In a zoo, there are some deer and some ducks, only. If the total number of heads counted in the zoo is 36 and total number of feet counted is 100, then...
A two-digit number '8d' is completely divisible by '4'. When the same number is divided by '3', there is a remainder of '1'. Find the value of 'd'.
- 'N' is the largest three-digit number that leaves 4 as a remainder when divided by 8, 14 and 10. Find the sum of digits of 'N'.
What is the least positive number which leaves remainders 5, 7, and 8 when divided by 6, 8, and 9 respectively?
If the 4-digit number r76s is exactly divisible by 9, what is the least value of (r + s)?
What is the average of all the prime numbers which are less than 35?
