Answer:
Option (c) is correct
Step-by-step explanation:
Case (a)
A = 3 + 5i = (3, 5)
B = 2 + 2i = (2, 2)
C = 5i = (0, 5)
Use the distance formula to find the distance between two points
![AB = \sqrt{(2-3)^{2}+(2-5)^{2}}=\sqrt{10}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%282-3%29%5E%7B2%7D%2B%282-5%29%5E%7B2%7D%7D%3D%5Csqrt%7B10%7D)
![BC = \sqrt{(0-2)^{2}+(5-2)^{2}}=\sqrt{13}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%280-2%29%5E%7B2%7D%2B%285-2%29%5E%7B2%7D%7D%3D%5Csqrt%7B13%7D)
![CA = \sqrt{(0-3)^{2}+(5-5)^{2}}=\sqrt{9}](https://tex.z-dn.net/?f=CA%20%3D%20%5Csqrt%7B%280-3%29%5E%7B2%7D%2B%285-5%29%5E%7B2%7D%7D%3D%5Csqrt%7B9%7D)
For the triangle to be right angles triangle
![BC^{2}=AB^{2}+CA^{2}](https://tex.z-dn.net/?f=BC%5E%7B2%7D%3DAB%5E%7B2%7D%2BCA%5E%7B2%7D)
Here, it is not valid, so these are not the points of a right angled triangle.
Case (b)
A = 2i = (0, 2)
B = 3 + 5i = (3, 5)
C = 4 + i = (4, 1)
Use the distance formula to find the distance between two points
![AB = \sqrt{(3-0)^{2}+(5-2)^{2}}=\sqrt{18}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%283-0%29%5E%7B2%7D%2B%285-2%29%5E%7B2%7D%7D%3D%5Csqrt%7B18%7D)
![BC = \sqrt{(4-3)^{2}+(1-5)^{2}}=\sqrt{17}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%284-3%29%5E%7B2%7D%2B%281-5%29%5E%7B2%7D%7D%3D%5Csqrt%7B17%7D)
![CA = \sqrt{(4-0)^{2}+(1-2)^{2}}=\sqrt{17}](https://tex.z-dn.net/?f=CA%20%3D%20%5Csqrt%7B%284-0%29%5E%7B2%7D%2B%281-2%29%5E%7B2%7D%7D%3D%5Csqrt%7B17%7D)
For the triangle to be right angles triangle
![AB^{2}=BC^{2}+CA^{2}](https://tex.z-dn.net/?f=AB%5E%7B2%7D%3DBC%5E%7B2%7D%2BCA%5E%7B2%7D)
Here, it is not valid, so these are not the points of a right angled triangle.
Case (c)
A = 6 + 4i = (6, 4)
B = 7 + 5i = (7, 5)
C = 8 + 4i = (8, 4)
Use the distance formula to find the distance between two points
![AB = \sqrt{(7-6)^{2}+(5-4)^{2}}=\sqrt{2}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%287-6%29%5E%7B2%7D%2B%285-4%29%5E%7B2%7D%7D%3D%5Csqrt%7B2%7D)
![BC = \sqrt{(8-7)^{2}+(4-5)^{2}}=\sqrt{2}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%288-7%29%5E%7B2%7D%2B%284-5%29%5E%7B2%7D%7D%3D%5Csqrt%7B2%7D)
![CA = \sqrt{(8-6)^{2}+(4-4)^{2}}=\sqrt{4}](https://tex.z-dn.net/?f=CA%20%3D%20%5Csqrt%7B%288-6%29%5E%7B2%7D%2B%284-4%29%5E%7B2%7D%7D%3D%5Csqrt%7B4%7D)
For the triangle to be right angles triangle
![CA^{2}=BC^{2}+AB^{2}](https://tex.z-dn.net/?f=CA%5E%7B2%7D%3DBC%5E%7B2%7D%2BAB%5E%7B2%7D)
Here, it is valid, so these are the points of a right angled triangle.
I love this unit a-lot (super fun)
So Congruent/Congruence is, For example If you have two triangles on a coordinates grid with the same coordinates than that would mean they're congruent. Shortened down would be
Same shape same coordinates same dimension same size (same everything)
Transformations would be Rotating a shape clockwise(CW)...right) or counterclockwise(CC Left)
Or Dilation which is making the shape smaller or bigger based on a scale factor.
Or reflection
How you would perform Reflection is reflect the shape over either the X-axis
Or the Y-axis
How you would perform a Translation would be to literally move the shape right left up or down.
How you would perform a Dilation(scaling) would be to pick a scale factor and either decrease or increase the size of the shape according to the scale factor number
How you would perform a Rotation would be to pick a point of rotation (P.O.R) and then pick your measure º such as 90º clockwise and rotate accordingly.
Hope it helps :)
<span>x : y is equal to 12 : 8. These can be reduced or cancelled down to 3 : 2 in the same proportions. Therefore, when y is 12, you have to multiply the smallest value y can be by 6, and must do the same to the smallest x value to retain the proportions. x = 18 when y = 12.</span>
-2 is the solution to this. The reason is is that if you do trail and error and plug in all of the numbers, you would get an answer of 16 and 16 as it shows on the table. And 16 = 16, so this is right!
Hope this helped! If it didn't, then please tell me what went wrong so I can fix it.
Answer:
-25=x
Step-by-step explanation:
20=10x-6(2x+5)
20=10x-12x-30
20=-2x-30
+30 +30
____________
50=-2x
÷-2 ÷-2
___________
-25=x
Hope this helps :D