A(3,5)and C(7,9) are the opposite vertices of a rhombus ABCD.find the equation of diagonal BD.
1 answer:
Answer:
y = 12 - x
Step-by-step explanation:
The diagonals of a rhombus bisect each other at right angles,
Thus, segment BD is a line perpendicular to AC and passing through the midpoint of AC.
1. Find the midpoint of AC
The midpoint of two points is half-way between their x- and y-values.
For the x-coordinate,
(x₂ + x₁)/2 = (7 + 3)/2 = 10/2 = 5
For the y-coordinate,
(y₂ + y₁)/2 = (9 + 5)/2 = 14/2 = 7
The coordinates of the midpoint are (5,7).
2. Calculate the equation of the diagonal BD
(a) Slope of AC
m₁ = Δy/Δx = (y₂ -y₁)/(x₂ - x₁) = (9 - 5)/(7 - 3) = 4/4 = 1
(b) Slope of BD
The slope m₂ of the perpendicular line BD must be the negative reciprocal of the slope of AC.
m₁ = -1/m₁ = -1
(c) Calculate the y-intercept of BD
The general equation for a straight line is
y = mx + b
Insert point (5,7).
7 = -1×5 + b
7 = -5 + b
b = 12
The y-intercept is (0,12).
(d) Write the equation for the line
y = -x + 12 or y = 12 - x
Points B and D can be any two points on the line that are equidistant from Point O, as shown in the Figure below.
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Answer:
z=1.59
If we compare the p value and the significance level given we see that
so we can conclude that we fail to reject the null hypothesis, so we can conclude that the mean repellency of the new bug repellent is greater than 89% at 0.025 of signficance.
Step-by-step explanation:
1) Data given and notation
represent the mean effectiveness of a new bug repellent for the sample
represent the population standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean repellency of the new bug repellent is greater than 89% or 0.89, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, and the sample size <30, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
First we need to calculate the degrees of freedom given by:
Since is a one-side upper test the p value would be:
In Excel we can use the following formula to find the p value "=1-T.DIST(1.59;17;TRUE)"
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we fail to reject the null hypothesis, so we can conclude that the mean repellency of the new bug repellent is greater than 89% at 0.025 of signficance.