A, B and C are the vertices of a triangle.
1 answer:
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
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Answer:
The width of the border can be 9 feet or 3.5 feet.
Step-by-step explanation:
Let the width be x
Length of room = 10 feet
Breadth of room = 15 feet
Length of rug = 10-2x
Breadth of rug = 15-2x
Area of rug =
We are given that the area of the rug is 24 square feet.
So, ---A
Substitute x =9 in A
LHS = RHS
Substitute x = 3.5
LHS = RHS
So, The width of the border can be 9 feet or 3.5 feet.
Answer:
Step-by-step explanation:
Notice that is a right triangle where its hypotenuse is
. We can also see that
. For this we must use the Pythagorean Theorem.
Recall:
The Pythagorean Theorem states that if you have a right triangle, the principal square root of the sum of the squares of each leg is the length the hypotenuse.
We can see that and