Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
On this exercise is given that a triangle with vertices (-2,1), (8,4), and (3,0) was dilated by a scale factor of four, and it is asked to find the vertices of the image of the triangle after the dilation occurred.
Pre-image Image
(-2,1) -- (-2*4,1*4) -- (-8,4)
(8,4) -- (8*4,4*4) -- (32,16)
(3,0) -- (3*4,0*4) -- (12,0)
The coordinates representing the vertices of the triangle's image are (-8,4), (32,16), and (12,0); meaning that the ordered pair which is not a coordinate for a point in the triangle's image is (2,1).
Answer:
Step-by-step explanation:
you know ; for all reals a ; cos(π/2 - a) = sin(a)
so : sin(5x+15) = cos(π/2-(5x+15) ) = cos(π/2-5x-15)
sin(5x+15)=cos(4x−6) eqivaut : cos(π/2-5x-15) = cos(4x−6)
note : cos(a)=cos(b) : a= b +2kπ or a= - b +2kπ ....k in Z
π/2-5x-15 = 4x−6 + 2kπ or π/2-5x-15 = - (4x−6) + 2kπ....k in Z
continue calculate : x .......
24.) y = mx + b
slope(m) = 0.25
(0,4)...x = 0 and y = 4
now we sub and find b, the y int
4 = 0.25(0) + b
4 = b
so ur equation is : y = 0.25x + 4
26.) y = mx + b
slope(m) = 3/2
(-5,1)....x = -5 and y = 1
sub and find b, the y int
1 = 3/2(-5) + b
1 = - 15/2 + b
1 + 15/2 = b
2/2 + 15/2 = b
17/2 = b
ur equation is : y = 3/2x + 17/2
28.) y = mx + b
slope(m) = 4
(0,0)...x = 0 and y = 0
time to sub
0 - 4(0) + b
0 = b
so ur equation is : y = 4x + 0.....or just y = 4x
30.) (7,1)(7,8)....notice how the x's are the exact same number....this
means that ur line is a vertical line with a slope that is undefined.
ur equation is : x = 7
32.) (-2,-3)(0,0)
slope = (0 - (-3) / (0 - (-2) = (0 + 3) /(0 + 2) = 3/2
y = mx + b
slope(m) = 3/2
(0,0)...x = 0 and y = 0
sub
0 = 3/2(0) + b
0 = b
ur equation is : y = 3/2x + 0 or just y = 3/2x
34.) (1/3,0)(0,-1/4)
slope = (-1/4 - 0) / (0 - 1/3) = (-1/4)/(-1/3) = -1/4 * -3 = 3/4
y = mx + b
slope(m) = 3/4
(0,-1/4)...x = 0 and y = -1/4
sub
-1/4 = 3/4(0) + b
-1/4 = b
so ur equation is : y = 3/4x - 1/4
If you divided 28 by 2 you will get 14 then times that by 5 and you will get 70 that is how much 5 will be
