Question

The points D(8, -4), E(8, 2), and F (1, -4) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.

Answer 1

To find the perimeter of the triangle formed by points D(8, -4), E(8, 2), and F(1, -4), calculate the length of each side by using the distance formula or calculating the differences in coordinates. Then, add up the lengths of all three sides to find the perimeter.

Step-by-step explanation:

To find the perimeter of the triangle formed by points D(8, -4), E(8, 2), and F(1, -4), we need to calculate the length of each side of the triangle and then add them up. First, let's calculate the length of side DE. The coordinates of D and E have the same x-coordinate (8), so the length is the difference between their y-coordinates, which is 2 - (-4) = 6.

Next, let's calculate the length of side EF. The coordinates of E and F have the same y-coordinate (-4), so the length is the difference between their x-coordinates, which is 1 - 8 = -7. Since length cannot be negative, we take the absolute value, which is 7.

Lastly, let's calculate the length of side FD. The coordinates of F and D have different x and y-coordinates, so we use the distance formula. The distance formula is: Square root of [(x2 - x1)^2 + (y2 - y1)^2].

Now we can find the perimeter by adding up the lengths of all three sides: 6 + 7 + 7 = 20 units.

Answer 2

The perimeter of triangle DEF is approximately 10.6 units.

Step-by-step explanation:

The coordinates of the vertices D(8, -4), E(8, 2), and F(1, -4) are plotted on the coordinate plane. The triangle formed by connecting these points is then graphically represented. To find the perimeter of the triangle, we calculate the distance between each pair of vertices and sum them up.

The distance between two points (x₁, y₁) and (x₂, y₂) in a Cartesian plane is given by the distance formula.

[d = sqrt{(x₂ - x₁)² + (y₂ - y₁)²}

[d_{DE} = sqrt{(8 - 8)² + (2 - (-4))²} = sqrt{36} = 6]

[d_{EF} = sqrt{(1 - 8)² + ((-4) - 2)²} = sqrt{50} approx 7.1]

[d_{FD} = sqrt{(1 - 8)² + ((-4) - (-4))²} = sqrt{49} = 7]

The perimeter P is the sum of these distances.

[P = d_{DE} + d_{EF} + d_{FD} = 6 + 7.1 + 7 approx 20.1]

Rounding to the nearest tenth, the perimeter of triangle DEF is approximately 10.6 units. This value represents the total length of the three sides of the triangle.