Answer:
3.14 or π (It's the same thing)
Step-by-step explanation:
If you divide the circumference by its diameter, the constant ratio is called Pi
Answer:
a: vertical stretch
h: horizontal translation (remember not to get signs mixed up!)
k: vertical translation
Answer:
A' ( -12 , -12 )
B' ( 6 , -3 )
C' ( 3 , 3 )
Step-by-step explanation:
To find the coordinates of a point after a dilation simply multiply the x and y values of the points by the scale factor
Points: A(-8,-8) B(4,-2) C(2,2)
Scale factor: 1.5
Coordinates after the dilation
A' = (-8,-8) --------> (-8 * 1.5 , -8 * 1.5 ) ------------> (-12 , -12)
B' = (4,-2) ---------> (4 * 1.5 , -2 * 1.5) -----------> (6 , -3 )
C' = (2 , 2) ----------> (2 * 1.5 , 2 * 1.5) -----------> (3, 3)
So inclusion the coordinates of ABC after a dilation centered at the origin with a scale factor of 1.5 are A' ( -12 , -12 ) B' ( 6 , -3 ) C' ( 3 , 3 )
Answer:
Is this the inter question
Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
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Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
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We have the two equations x+y = 180 and y+z = 180 to form this system of equations

Which is really the same as this system

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.