Question

Show the mathematical calculations that demonstrate that you understand how to classify a figure on the coordinateplane. Refer to the rubric to understand how to structure your response. Submit your answers by either scanning in adocument or linking to a digital document that you create online.Classify each triangle that is described below. State a) your classification; b) your justification; c) your reasoningbased on the stated justification;You must justify you answer showing at least five detailed calculations using the distance formula, Pythagoreantheorem, and/or slope formula. Each of your calculations must list the formula, and show substitution, andsimplification steps.• Triangle ABC: A(-1,3); B(-1,-3); C(-6, 0)Triangle DEF: D: (4,4); E(6,2); F(1,-3)Triangle JKL: J: (8,6); K:(1,0); L:(0,2)Triangle RST: R:(-2,6); S(62); T(-3,3)/100

Answer 1

sides areTriangle ABC: A(-1,3); B(-1,-3); C(-6, 0)

using distance formula

`d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}`

Substitute the points and we can get

Distance of A and B is 6

Distance of A and C is 5.83

Distance of B and C is 5.83

Since two sides are equal, the triangle is an isosceles

Triangle DEF: D: (4,4); E(6,2); F(1,-3)

using distance formula

`d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}`

Substitute the points and we can get

Distance of D and E is 2.83 (square root of 8)

Distance of D and F is 7.62 (square root of 58)

Distance of E and F is 7.07 (square root of 50)

Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.

`c^2=a^2+b^2`

Using the calculated lengths/distances

the longest is set to hypotenuse

`(\sqrt[]{58})^2=(\sqrt[]{50})^2+\text{ }(\sqrt[]{8})^2`

Since the triangle DEF follows Pythagorean theorem. It is a right triangle.

Triangle JKL: J: (8,6); K:(1,0); L:(0,2)

using distance formula

`d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}`

Substitute the points and we can get

Distance of J and K is square root of 85

Distance of J and L is square root of 80

Distance of K and L is square root of 5

Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.

`c^2=a^2+b^2`

Using the calculated lengths/distances

the longest is set to hypotenuse

`(\sqrt[]{85})^2=(\sqrt[]{80})^2+\text{ }(\sqrt[]{5})^2`

Since the triangle JKL follows Pythagorean theorem. It is a right triangle.

Triangle RST: R:(-2,6); S(6, 2); T(-3,3)

using distance formula

`d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{}_{})^2}`

Substitute the points and we can get

Distance of R and S is square root of 80

Distance of R and T is square root of 10

Distance of S and T is square root of 82

Since it is not conclusive what type of triangle this is. We will use Pythagorean to check if this is a right triangle. since this theorem work on right triangles.

`c^2=a^2+b^2`

Using the calculated lengths/distances

the longest is set to hypotenuse

`(\sqrt[]{82})^2=(\sqrt[]{80})^2+\text{ }(\sqrt[]{10})^2`

Since the triangle RST does not follow Pythagorean theorem. It is a scalene triangle. No sidesare equal. no angles are equal