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The equation of BD is A(-8;6),B,C and D(3;9) are the vertices of a rhombus. is 3x-y=0. The diagonals of the rhombus intersect at point K. 4.1 Calculate the perimeter of ABCD. Leave your answer in simplest surd

User Jyoung
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Answer and Step-by-step explanation:

To calculate the perimeter of the rhombus ABCD, we need to find the lengths of all four sides and then add them together.

Given that point A is (-8, 6) and point D is (3, 9), we can calculate the lengths of sides AB, BC, CD, and DA using the distance formula:

1. Calculate the length of side AB:

- The distance between points A(-8, 6) and B(x, y) is given by the equation:

sqrt((x - (-8))^2 + (y - 6)^2) = sqrt((x + 8)^2 + (y - 6)^2)

2. Calculate the length of side BC:

- Since point C lies on the line y = 3x, we can substitute the x-coordinate of point B into the equation y = 3x to find the y-coordinate of point C.

- The distance between points B(x, y) and C(x, 3x) is given by the equation:

sqrt((x - x)^2 + (y - 3x)^2) = sqrt(0^2 + (y - 3x)^2)

3. Calculate the length of side CD:

- The distance between points C(x, 3x) and D(3, 9) is given by the equation:

sqrt((x - 3)^2 + (3x - 9)^2)

4. Calculate the length of side DA:

- The distance between points D(3, 9) and A(-8, 6) is given by the equation:

sqrt((3 - (-8))^2 + (9 - 6)^2) = sqrt((3 + 8)^2 + (9 - 6)^2)

Once you have calculated the lengths of all four sides, add them together to find the perimeter of the rhombus ABCD. Leave your answer in simplest surd form.

User Squeegy
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