Question

Mark the points (10, 14), (15, 11.11), and (10, 8.22). Enter the coordinates in the input window, if you wish. Then connect the points to form a triangle. Part A Measure the lengths of the sides of the triangle and record them in the table.

Answer 1

Answer:

The points form a equilateral triangle of side 5.78 units.

Step-by-step explanation:

The length of the sides of the triangle is calculated using the distance formula.

The distance between the points (x₁,y₁) and (x₂,y₂) is

$d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Now,

AB = $\sqrt{(11.11-14)^{2}+(15-10)^{2}}=\sqrt{8.3521+25} = \sqrt{33.3521}=5.78$

BC = $\sqrt{(8.22-11.11)^{2}+(10-15)^{2}}=\sqrt{8.3521+25} = \sqrt{33.3521}=5.78$

CA =  $\sqrt{(8.22-14)^{2}+(10-10)^{2}}=5.78$

The length of the sides of the triangle is 5.78. All the sides are equal in length. It is an equilateral triangle.