Answer:
(x - 8)² + (y + 6)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (8, - 6 ) , then
(x - 8)² + (y - (- 6))² = r² , that is
(x - 8)² + (y + 6)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = 
with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )
r = 
= 
= 
= 
= 
= 5
Then equation of circle is
(x - 8)² + (y + 6)² = 5² , that is
(x - 8)² + (y + 6)² = 25
9514 1404 393
Answer:
Any of ...
- rotation 180° about the center of symmetry
- reflection across the horizontal and vertical lines through the center of symmetry, in either order
- reflection across any horizontal line, translation to the left, and translation up or down to final position (depending on where the horizontal line is)
Step-by-step explanation:
The question is asking you what combinations of rotation, reflection, translation, and dilation will make the W have the position, orientation, and size of the M.
The image (M) is the same size as the preimage (W), so no dilation is involved.
The up-down orientation of the image is opposite that of the preimage, so reflection across a horizontal line, or rotation 180° will be involved. Depending on the line of reflection or the center of rotation, translation to the final image position may be required.
The preimage is symmetrical about a vertical centerline, so translation left or right can also be accomplished by reflection about a suitable vertical line.
_____
If you have trouble visualizing this, it can help to cut the letter from a piece of paper and manipulate it to model rotation, reflection, or translation.
When you multiply fractions all you need to do is multiply straight like lets say you have the fractions 1/3*1/2you multiply as if you would multiply normally like first the dominators 1*1=1 and now the numerators 3*2=6 now we put them in order 1/6.
Hope it helps.
To see if a pair of ratios is proportional... you need to compute for its cross products. If the cross products are equal then they are proportional.
a/b = c/d where ad = bc
a) 4/9 = 16/45 ⇒ 4*45 = 9*16 ⇒ 180 = 144 NOT PROPORTIONAL
b) 5/12 = 25/144 ⇒ 5*144 = 12*25 ⇒ 720 = 300 NOT PROPORTIONAL
c) 12/18 = 18/27 ⇒ 12*27 = 18*18 ⇒ 324 = 324 PROPORTIONAL
d)15/20 = 7/10 ⇒ 15*10 = 20*7 ⇒ 150 = 140 NOT PROPORTIONAL
