The area of the triangle whose vertices are given by the coordinates (1,2), (-4, -3) and (4, 1) is _

Question

The area of the triangle whose vertices are given by the coordinates (1,2), (-4, -3) and (4, 1) is ________.

Accepted Answer

{"type":"doc","content":[{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 1 (Area of Triangle Formula):"},{"text":" For a triangle with vertices ","type":"text"},{"attrs":{"latex":"(x_1, y_1)"},"type":"math_inline"},{"text":", ","type":"text"},{"attrs":{"latex":"(x_2, y_2)"},"type":"math_inline"},{"text":", and ","type":"text"},{"attrs":{"latex":"(x_3, y_3)"},"type":"math_inline"},{"text":", the area ","type":"text"},{"attrs":{"latex":"A"},"type":"math_inline"},{"text":" is given by the determinant formula:","type":"text"}]},{"attrs":{"latex":"A = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Substitute the Coordinates):","type":"text"},{"type":"text","text":" We substitute "},{"attrs":{"latex":"(1,2)"},"type":"math_inline"},{"type":"text","text":", "},{"attrs":{"latex":"(-4, -3)"},"type":"math_inline"},{"text":", and ","type":"text"},{"type":"math_inline","attrs":{"latex":"(4, 1)"}},{"text":" into the formula:","type":"text"}]},{"attrs":{"latex":"A = \frac{1}{2} |1(-3 - 1) + (-4)(1 - 2) + 4(2 - (-3))|"},"type":"math_block"},{"attrs":{"latex":"A = \frac{1}{2} |1(-4) + (-4)(-1) + 4(5)|"},"type":"math_block"},{"type":"math_block","attrs":{"latex":"A = \frac{1}{2} |-4 + 4 + 20|"}},{"attrs":{"latex":"A = \frac{1}{2} |20| = 10"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The area of the triangle is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"10","type":"text"},{"text":" sq. units.","type":"text"}],"type":"paragraph"}]}

Guide / Hint

Solution