Question

find the type of trians formed by the point q (_5,6) q (_4,_2)r (7,5)​

Answer 1

Given: Points - p(-5, 6), q(-4, -2), r(7, 5).

To find: The type of triangle formed.

Answer:

We'll be finding the distance between each point.

Distance formula:

$\sf \Bigg(x,\ y\Bigg)\ =\ \sqrt{\Bigg(x_2\ -\ x_1\Bigg)^2\ +\ \Bigg(y_2\ -\ y_1\Bigg)^2}$

Let's first find the distance between the points p(-5, 6) and q(-4, -2).

From those points,

$\bullet\ \sf x_1\ =\ -5\\\\\bullet\ x_2\ =\ -4\\\\\bullet\ y_1\ =\ 6\\\\\bullet\ y_2\ =\ -2$

Using them in the formula,

$\sf Distance\ =\ \sqrt{\Bigg(\Big(-4\ +\ 5\Big)^2\ +\ \Big(-2\ -\ 6\Big)^2\Bigg)}\\\\\\Distance\ =\ \sqrt{\Bigg(\Big(1\Big)^2\ +\ \Bigg(-8\Big)^2\Bigg)}\\\\\\Distance\ =\ \sqrt{\Bigg(1\ +\ 64\Bigg)}\\\\\\\bf Distance\ =\ 8.06\ units\ [approx]$

Now, the distance between the points q(-4, -2) and r(7, 5).

From those points,

$\bullet\ \sf\ x_1\ =\ -4\\\\\bullet\ x_2\ =\ 7 \\\\\bullet\ y_1\ =\ -2\\\\\bullet\ y_2\ =\ 5$

Using them in the formula,

$\sf Distance\ =\ \sqrt{\Bigg(7\ +\ 4\Bigg)^2\ +\ \Bigg(5\ +\ 2\Bigg)^2}\\\\\\Distance\ =\ \sqrt{\Bigg(11\Bigg)^2\ +\ \Bigg(7\Bigg)^2}\\\\\\Distance\ =\ \sqrt{\Bigg(121\ +\ 49\Bigg)}\\\\\\\bf Distance\ =\ 13.03\ [approx]$

Now, between the points r(7, 5) and p(-5, 6).

From those points,

$\bullet\ \sf x_1\ =\ 7\\\\\bullet\ x_2\ =\ -5\\\\\bullet\ y_1\ =\ 5\\\\\bullet\ y_2\ =\ 6$

Using them in the formula,

$\sf Distance\ =\ \sqrt{\Bigg(-5\ -\ 7\Bigg)^2\ +\ \Bigg(6\ -\ 5\Bigg)^2}\\\\\\Distance\ =\ \sqrt{\Bigg(-12\Bigg)^2\ +\ \Bigg(1\Bigg)^2}\\\\\\Distance\ =\ \sqrt{\Bigg(144\ +\ 1\Bigg)}\\\\\\Distance\ =\ \sqrt{\Bigg(145\Bigg)}\\\\\\\bf Distance\ =\ 12.04\ [approx]$

We have three sides of the triangle, measuring 8.06, 13.03 and 12.04.

• An equilateral triangle has all sides of equal measures.
• An isosceles triangle has two sides of equal measures.
• A scalene triangle has all sides of different measures.

Therefore, the triangle formed by the points p(-5, 6), q(-4, -2) and r(7, 5) is a scalene triangle.

Answer 2

Explanation:

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