Permutations an...

Find the area of the triangle whose vertices are $$(a, b + c), (a, b - c)$$ and $$(-a, c)$$.

Find the area of the right-angled triangle whose vertices are $$(2, -2)$$ , $$(-2, 1)$$ and $$(5, 2).$$

The  triangle with vertices A(4, 4), B(-2, -6) and C(4, -1) is shown in the diagram. The area of $$\Delta$$ ABC is _______

The coordinates of $$A$$ for which area of triangle, whose vertices are $$A(a, 2a),\  B(-2, 6)$$ and $$C(3, 1)$$ is $$10$$ square units, are:

The number of positive fractions $$\dfrac{m}{n}$$ such that $$\dfrac{1}{3}< \dfrac{m}{n}<1 $$ and having the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is:

$$(3, 1), (-3, 2)$$ and $$\displaystyle (0,2-\sqrt{3})$$ are the vertices of __________ triangle of area ___________.

Three points A, B and C have coordinates $$(a, b + c), \ (b, c + a)$$ and $$(c, a + b)$$, respectively. The area of the triangle ABC will be:

If the area of a triangle formed by the points (k, 2k) (-2, 6) and (3, 1) is 20 square units. Find the value of k.

If the coordinates of two points A and B are $$(3, 4)$$ and $$(5, -2)$$, respectively, then the coordinates of any point P if $$PA = PB$$ and area of $$\displaystyle \Delta PAB=10$$ is

Find pair of consecutive odd natural numbers, both of which are larger than 13 such that their sum is less than 40