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.
Statements:
P < Q < R < S ≤ B < H; S > N ≥ Y
Conclusions:
I) P < Y
II) R ≥ N
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and the...
Statements: P ≥ Q ≥ R = S, Q ≥ T > U ≥ V
Conclusion:
I. P ≥ V
II. P > V
Statements: J < K; L = M; K >N ≥ L
Conclusions:
I. J < L
II. N = M
Statements: M = N ≤ P = C > G, D ≥ M > T = F
Conclusion:
I. D ≥ N
II. N > F
III. F < P
Statements: A ≥ B ≥ Y = Z = M ≥ N ≤ E ≤ F = J
Conclusions:
I. F > Z
II. J ≤ Y
Which of the following expression symbols should replace the question mark(?) in the given expressions to make the expression C ≥ E as well as D > M d...
Statement: M < N; L ≥ U; L ≥ Q; U > N ≥ T
Conclusion:
I. N > Q
II. Q > T
Statements: X < H = U ≤ I < N = M, M > B ≥ V
Conclusions:
I. I > V
II. U ≥ MStatement: D > C > U < K > E > N < A
Conclusion:
I. D > N
II. D > A
