In this diagram, lines AC and DE are parallel and line DC is perpendicular to each of them. What is a reasonable estimate for th
1 answer:
The reasonable estimate for the length of side DE is 3 units
Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.
Using the similarity theorem of a triangle, this is expressed as:
AC = DE
Using the pythagoras theorem to get the length of AC:
AB^2 = AC^2 + BC^2
5^2 + AC^2 + 4^2
AC^2 = 25 - 16
AC^2 = 9
AC= 3
Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units
Learn more on similar shapes here: brainly.com/question/14285697
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FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula =
Now, plug the values into the formula, So,
distance =
=
=
=
=
=
So, the length of AB is.
<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.
Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint =
Now, equaling the ordered pair, we have,
.............equation (1)
................equation (2)
Now, taking equation (1)
Now, taking equation (2)
<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)
</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1
Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4
So, x=1 and y=4
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula =
Now, plug the values into the formula, So,
distance =
=
=
=
=
=
So, the length of AB is
<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.
Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint =
Now, equaling the ordered pair, we have,
Now, taking equation (1)
Now, taking equation (2)
<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)
</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1
Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4
So, x=1 and y=4