Question

find the perimeter of the triangle whose vertices are (-2,1),(4,6) and(6,3)

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Answer 1

Answer:

3

Step-by-step explanation:

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Answer 2

Given:

• A triangle formed by the coordinates (-2, 4), (4, 6) and (6, 3).

To find:

• The perimeter.

Answer:

To do so, we'll have to find the length of each side [distance between two points.]

Distance formula:

$\tt Distance\ =\ \sqrt{\Bigg(x_2\ -\ x_1\Bigg)^2\ +\ \Bigg(y_2\ -\ y_1\Bigg)^2}$

Let's first find the distance between the points (-2, 4) and (4, 6).

From those points,

$\tt x_1\ =\ -2\\\\x_2\ =\ 4\\\\y_1\ =\ 4\\\\y_2\ =\ 6$

Using them in the formula,

$\tt Distance\ =\ \sqrt{\Bigg(4\ +\ 2\Bigg)^2\ +\ \Bigg(6\ -\ 4\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(6\Bigg)^2\ +\ \Bigg(2\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(36\ +\ 4\Bigg)}\\\\\\\\\bf Distance\ =\ \sqrt{40}\ =\ 6.32\ units\ [approx.]$

Now, let's find the distance between the points (4, 6) and (6, 3).

From those points,

$\tt x_1\ =\ 4\\\\x_2\ =\ 6\\\\y_1\ =\ 6\\\\y_2\ =\ 3$

Using them in the formula,

$\tt Distance\ = \sqrt{\Bigg(6\ -\ 4\Bigg)^2\ +\ \Bigg(3\ -\ 6\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(2\Bigg)^2\ +\ \Bigg(-3\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(4\ +\ 9\Bigg)^2}\\\\\\\\\bf Distance\ =\ \sqrt{13}\ =\ 3.6\ units\ [approx.]$

Now, the distance between the points (6, 3) and (-2, 4).

From those points,

$\tt x_1\ =\ 6\\\\x_2\ =\ -2\\\\y_1\ =\ 3\\\\y_2\ =\ 4$

Using them in the formula,

$\tt Distance\ =\ \sqrt{\Bigg(-2\ -\ 6\Bigg)^2\ +\ \Bigg(4\ -\ 3\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(-8\Bigg)^2\ +\ \Bigg(1\Bigg)^2}\\\\\\\\Distance\ =\ \sqrt{\Bigg(64\ +\ 1\Bigg)}\\\\\\\\\bf Distance\ =\ \sqrt{65}\ =\ 8.06\ units\ [approx.]$

Now, to find the perimeter.

Perimeter = Sum of the lengths of all sides

Perimeter = 6.32 + 3.6 + 8.06

Perimeter = 17.98

Therefore, the perimeter of the triangle formed by the points (-2, 4), (4, 6) and (6, 3) = 17.98 units.