What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? Point: (7,3)
1 answer:
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Answer:
Option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.
Step-by-step explanation:
As the assumption quadrilateral ABCD is shown in figure a.
First located the center of the dilation which is located at (2,2) as shown in figure b.
The next thing we want to do is to determine the distance of the center of dilation to each of the points of quadrilateral ABCD as shown in figure b.
Let’s just start with the distance from the center to the point A, but notice we don’t have to move up and down in y direction. So, what we have to do is to increase this by the factor 2. Because this horizontal distance is 1 i.e. the distance from dilation center (2,2) to point A, we just have to multiply by 2 which would be a distance of 2 and this point right here will be the new location of point A’ (0,2).
And the distance from the center to the point C is the horizontal distance of 2 i.e. the distance from dilation center (2,2) to point C, we just have to multiply by 2 which would be a distance of 4 and this point right here will be the new location of point C’ (6,2).
And the distance from the center to the point B is the upward vertical distance of 1 i.e. the distance from dilation center (2,2) to point B, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point B’ (2,4).
And similarly the distance from the center to the point D is the downward vertical distance of 1 i.e. the distance from dilation center (2,2) to point D, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point D’ (2,0).
So, Quadrilateral A'B'C'D' is dilated by a scale factor of 2 centered around (2, 2).
Just notice in figure b that the segment B'D' will run through (2,2) and will be longer than the segment BD.
<u>So,option (B) is true</u> <u>i.e segment</u><u> </u><u>B'D' will run through (2,2) and will be longer than the segment BD.</u>
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Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13