In rhombus ABCD, diagonals AC and BD are drawn. If the rhombus is graphed on a coordinate plane the slope of AC is 3/5. What is the slope of BD? Explain how you know.
diagonals of a rhombus are perpendicular bisectors of each other
so, the slope of BD = -1/(3/5) = -5/3
It sure did! Thank you! :)
To find the slope of BD in a rhombus ABCD when the slope of AC is known, we need to use some properties of rhombuses.
In a rhombus, the diagonals are perpendicular bisectors of each other. This means that the product of their slopes is -1.
Let's break down the steps to find the slope of BD:
Step 1: Identify the given slope of AC.
A slope of 3/5 is given for the diagonal AC.
Step 2: Use the property that the product of the slopes of perpendicular lines is -1.
Since AC and BD are perpendicular bisectors, the product of their slopes is -1.
So, we have:
Slope of AC * Slope of BD = -1
Step 3: Solve for the slope of BD.
Plugging in the given slope of AC, we get:
(3/5) * Slope of BD = -1
To solve for the slope of BD, we can isolate it by dividing both sides of the equation by (3/5):
Slope of BD = (-1) / (3/5)
Simplifying, we can multiply by the reciprocal of (3/5):
Slope of BD = (-1) * (5/3) = -5/3
Therefore, the slope of BD is -5/3.
In summary, the slope of BD in the given rhombus ABCD is -5/3, and we found this by utilizing the property that the diagonals of a rhombus are perpendicular bisectors of each other.