Question
Find the area of the triangle formed by the points A(2,
3), B(-1, -4), and C(5, -2).Solution
The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by: Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Substituting the given points: Area = 1/2 * |2(-4 - (-2)) + (-1)(-2 - 3) + 5(3 - (-4))| = 1/2 * |2(-2) + (-1)(-5) + 5(7)| = 1/2 * |-4 + 5 + 35| = 1/2 * |36| = 18 square units.
‘a’ is directly proportional to ‘b’. If at a=30, the value of ‘b’ is 20% greater than ‘a’, then find the value of ‘a’ when b=54.
...If a + `1/b` = 1 and b + `1/c` =1 , then the value of c + `1/a` is
The average of three numbers a, b and c is 2 more than c. The average of a and b is 48. If d is 10 less than c, then the average of c and d is:
√(92×8 ×52+700) = ?
If x4 + x - 4 = 47 then find the value of (x + x-1).
If a + b + c = 5, a³ + b³ + c³ = 85 and abc =25, then find the value of a² + b² + c² – ab –bc – ca
- If x + 4y = 26 and 4x + y = 41, then find the value of (x - y).
- If p = 25 - q - r and pq + r(p + q) = 256, then find the value of (p² + q² + r²).
If 10x2 – 6xy+y² – 4x+4= 0, then find the value of (3x+2y).
Find the value of ‘x’ in the given expression:
(49/16)x × (64/343)x-1 = 4/7
