Using pythagorean's theorem
a^2+b^2=c^2
a being 3
b being 4
we'll get
9+16=25
where 5 is the hypotenuse and also c.
c^2 = 5^2
17. RQ is the same as PS.
PS = -1 + 4x
RQ = 3x + 3
-1 + 4x = 3x + 3
4x = 3x + 4
x = 4
Now plug that into RQ.
3(4) + 3 = RQ
15 = RQ
18. Angles G and E are equal to each other.
G = 5x - 9
E = 3x + 11
5x - 9 = 3x + 11
5x = 3x + 20
2x = 20
x = 10
Plug that x into G.
5(10) - 9
41 = G
19. TE and EV are equal to each other.
TE = 4 + 2x
EV = 4x - 4
4 + 2x = 4x - 4
2x = 4x - 8
-2x = -8
x = 4
Plug that into TE.
4 + 2(4)
12 = TE
20. DB and BF are equal.
DB = 5x - 1
BF = 5 + 3x
5x - 1 = 5 + 3x
5x = 6 + 3x
2x = 6
x = 3
Plug that into DB.
5(3) - 1
14 = DB
By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.
<h3>How to derive the equation of the axis of symmetry </h3>
In this question we know the locations of two points with the same y-value, which means that the axis of symmetry is parallel to the y-axis and that both points are equidistant. Thus, the axis of symmetry passes through the midpoint of the line segment whose ends are those points.
First, calculate the coordinates of the midpoint by the midpoint formula:
M(x, y) = 0.5 · (- 7, 11) + 0.5 · (3, 11)
M(x, y) = (- 2, 11)
Second, look for the first coordinate of the midpoint and derive the equation of the line associated with the axis of symmetry:
x = - 2
By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.
To learn more on axes of symmetry: brainly.com/question/11957987
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