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

The points form a equilateral triangle of side 5.78 units.

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)}=√(8.3521+25) = √(33.3521)=5.78`

BC =
`\sqrt{(8.22-11.11)^(2)+(10-15)^(2)}=√(8.3521+25) = √(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.