Question

Two similar triangles are drawn in the coordinate plane: ΔABC and ΔA1B1C11) Calculate the lengths of the side BC and the hypotenuse AC. 2) Calculate the area of ΔABC. 3) Calculate how many times the sides of ΔA1B1C1 are shorter than the corresponding sides of ΔABC. 4) Calculate the area of ΔA1B1C1.

Answer 1

Step-by-step explanation:

a) Here, we want to calculate the length of the sides of the triangle ABC

Firstly, we need to get the coordinates of the points

A (-7,-3)

B(-8,3)

C (-5,3)

To find the length of any of the sides, we use the distance between points formula

That would be:

`D=\text{ }\sqrt{(x_2-x_1)\placeholder{⬚}^2+(y_2-y_1)\placeholder{⬚}^2}`

For BC, we have:

`\begin{gathered} BC\text{ = }\sqrt{(-5+8)\placeholder{⬚}^2-(3-3)\placeholder{⬚}^2} \\ BC\text{ = 3 units} \end{gathered}`

For AC, we have:

`\begin{gathered} AC\text{ = }\sqrt{(-5_+7)\placeholder{⬚}^2+(3+3)\placeholder{⬚}^2} \\ AC\text{ = }\sqrt{4\text{ + 36}} \\ AC\text{ = }√(40) \end{gathered}`

b) Here, we want to calculate the area of triangle ABC.

We can use Heron's formula here: