Question

The point moves such that the area of the triangle formed by the points 1, 5 and 3, - 7 21 square units the locus of the point is

Answer 1

Finding locus of a point

Given: A point moves in such way that the area bounded by that point and other two points (1, 5) and (3, - 7) is 21 square units.

To find: The locus of the moving point (or vertex).

Solution:

Let us take the variable point (a, b).

Then the area of the triangle formed by the points (a, b), (1, 5) and (3, - 7) is

$=\frac{1}{2}|\left|\begin{array}{ccc}a&b&1\\1&5&1\\3&-7&1\end{array}\right||$ square units

= 1/2 * | 12a + 2b - 22 | square units, expanding along the first row

= | 6a + b - 11 | square units

Here given,

$\quad$ | 6a + b - 11 | = 21

or, 6a + b = ± 21 + 11

i.e., 6a + b = 32 or, 6a + b + 10 = 0

Therefore the locus of the moving point is

$\quad$6x + y = 32 or 6x + y + 10 = 0.

Answer 2

Answer:

Hey ur answrr

Step-by-step explanation:

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