Polygon P'Q'R'S'T' shown on the grid below is an image of polygon PQRST after dilation with a scale factor of 3, keeping the ori
2 answers:
Answer:
The correct option is 4. The lengths of side SR and side S'R' are in the ratio 1:3.
Step-by-step explanation:
The vertices of polygon are P(0,-3), Q(3,-2), R(3,1), S(0,2), T(-2,0).
The vertices of image are P'(0,-9), Q'(9,-6), R'(9,3), S'(0,6), T'(-6,0).
It is given that polygon P'Q'R'S'T' is the image of polygon PQRST after dilation with a scale factor of 3. It means both polygons are similar.
The corresponding angles of similar figure and same and the corresponding sides are proportional. It means the sides of image are three times of the corresponding sides of pre-image.
SR and S'R' are corresponding sides.
The lengths of side SR and side S'R' are in the ratio 1:3.
Therefore the correct option is 4.
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The answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
What is slope of a line segment ?
The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).
Let's solve the given parts based on the above data.
a.
The length of the line segment will be given by :
YZ =
YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}
YZ = √ (-8)² + 2²)
YZ = √68
YZ = 8.24 units
b.
The midpoint (say M) of the line segment will be given by :
M = ( )
M = [(2-6)/2 , (-3-1)/2]
M = ( -2 , -2 )
c.
And the equation of line passing through points Y and Z will be :
= m (
)
Let's calculate value of slope (m) firstly which will be :
m =() / (
)
m = ( -1 + 3 ) / (-6 - 2)
m = 2 / -8
m = -1 / 4
or
m = -0.25
Using the value of slope (m) : we get the equation of line as :
= - 0.25 (
)
or
(y + 3) = - 0.25 ( x - 2)
y + 3 = -0.25 x + 0.50
or
y + 0.25 x - 2.5 = 0
If we multiply by 4 throughout the equation ; then the equation of line can also be written as :
4y + x - 10 = 0
Therefore the answers will be :
a. The length of the line segment will be equal to 8.24 units.
b. The midpoint of the line segment will be ( -2 , -2 ).
c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0
Learn more about line segment here ;
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