i did the assignment on edge, i hope this helps! :)
On a coordinate plane, square P Q R S is shown. It has points (0, 4), (4, 4), (0, 0), and (4, 0).
Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other.
Step 1: Calculate the slope of the diagonals.
The slope of diagonal PS is . -1
The slope of diagonal QR is . 1
Step 2: Calculate the midpoint of the diagonals.
The midpoint of PS is . (2,2)
The midpoint of QR is . (2,2)
The diagonals of the square are perpendicular bisectors because the diagonals are . perpendicular and share the same midpoint
answer: Option A
Given that a square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year
Each diagonal = 9 inches
Using Pythagorean theorem for right triangle with two sides and one diagonal we get
Iron rods needed for square with two diagonals
= perimeter of square + length of 2 diagonals
Rounding off gives
43.5 inches Option A
Definition of perpendicular
we know that
The approximate total length of iron edging needed to create the square frame and the two diagonals is given by the formula
b is the length side of the square
d is the diagonal of the square
----> given problem
Find the value of b
Remember that the diagonal in a square is given by
substitute the given value of d
solve for b
Find the total length
The arrangement below make it possible
As describe in step by step explanation
5.-They need to have the same sign, because this is the only way you can compensate with other opposite charge
We have to reasoning this way. Let say the empty corner is at the upper right of the square. if we call F1 and F2 forces acting in this point, due to charges of the left and down corners of the square respectivly. F1 will have direction of x axis and F2 will have direction of y axis. Now in order to cancel these two forces, we need:
1.-Charges in left and down coners, must be of the same sign and magnitude
2.-the charge in diagonal opposite corner have to be of opposite sign and bigger charge than the two previous charges.
How big it need to be ??
E₁ = Ex = K*q₁/d² E₂ = Ey = K*q₂/d² (1) q₁ = q₂ = q
distance between empty corner and its opposite corner is:
L = √ d² + d² ⇒ L = √2 * d
cos 45⁸ = sin 45⁸ = √2/2
E₃ ( field due to charge in opposite corner) is:
E₃ =K* q/ 2 * d²
And E₃ₓ = E₃y = cos 45⁸* E₃
E₃ₓ = [ K*q/2 *d² ]* √2/2
E₃ₓ = K*q *√2/4*d²
Now if we compare E₃ₓ with Ex = K*q₁/d² equation (1)
q*√2/4 = q₁
q = 4*q₁/√2
5) definition of perpendicularity.
In this question actually we have to fill the blanks and complete the sentence where it is looking like incomplete.
So , at first (1) we see that it is given that if we consider triangle AEB and Triangle AED we see that side AB side is congruent to side AD.
(2) We know that side AE is congruent to side AE by using the Reflexive property
(3)and side DE is congruent to side BE because the diagonals of a square bisect each other.
(4)Therefor triangle AEB is congruent to trianlgle AED by SSS congruency.
(5) so by CPCT , the angle AED and AEB are a linear pair and the measure of these angle will be 90 because ABCD is a square and thus diagonal AC is perpendicular to diagonal BD by the definition of perpendicularity.
5) definition of perpendicularity.
The slope of diagonal PS is -1. The The slope of diagonal QR is 1. The midpoint of PS is (2,2). Midpoint of QR is (2,2).
The given vertices are P (0,4), Q (4,4), R (0,0) and S (4,0).
If a line passing through the point and , then the slope of the line is,
The slope of diagonal PS is,
The slope of diagonal QR is,
The slope of both diagonals are 1 and -1, therefore the product of their slopes is -1. So, the diagonals are perpendicular to each other.
The formula for midpoint is,
The midpoint of PS is,
The midpoint of QR is,
The midpoint of both diagonals are same, therefore diagonals are bisecting each other.
Therefore, the slope of diagonal PS is -1. The The slope of diagonal QR is 1. The midpoint of PS is (2,2). Midpoint of QR is (2,2).
it is d=8cm
I hope this helps!!!