Answer:
(A)Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent.
![\dfrac{UW}{XZ}=\dfrac{WV}{ZY}=\dfrac{UV}{XY}](https://tex.z-dn.net/?f=%5Cdfrac%7BUW%7D%7BXZ%7D%3D%5Cdfrac%7BWV%7D%7BZY%7D%3D%5Cdfrac%7BUV%7D%7BXY%7D)
Step-by-step explanation:
In Triangles WUV and XZY:
![\angle VUW$ and \angle YXZ$ are congruent. \\\angle U W V$ and \angle X Z Y$ are congruent.\\ \angle U V W$ and \angle Z Y X$ are congruent.](https://tex.z-dn.net/?f=%5Cangle%20VUW%24%20and%20%5Cangle%20YXZ%24%20are%20congruent.%20%5C%5C%5Cangle%20U%20W%20V%24%20and%20%5Cangle%20X%20Z%20Y%24%20are%20congruent.%5C%5C%20%5Cangle%20U%20V%20W%24%20and%20%5Cangle%20Z%20Y%20X%24%20are%20congruent.)
Therefore:
![\triangle UWV \cong \triangle XZY](https://tex.z-dn.net/?f=%5Ctriangle%20UWV%20%5Ccong%20%20%5Ctriangle%20XZY)
To show that the triangles are similar by the SSS similarity theorem, we have:
![\dfrac{UW}{XZ}=\dfrac{WV}{ZY}=\dfrac{UV}{XY}](https://tex.z-dn.net/?f=%5Cdfrac%7BUW%7D%7BXZ%7D%3D%5Cdfrac%7BWV%7D%7BZY%7D%3D%5Cdfrac%7BUV%7D%7BXY%7D)
As a check:
![\dfrac{UW}{XZ}=\dfrac{40}{32}=1.25\\\\\dfrac{WV}{ZY}=\dfrac{60}{48}=1.25\\\\\dfrac{UV}{XY}=\dfrac{50}{40}=1.25](https://tex.z-dn.net/?f=%5Cdfrac%7BUW%7D%7BXZ%7D%3D%5Cdfrac%7B40%7D%7B32%7D%3D1.25%5C%5C%5C%5C%5Cdfrac%7BWV%7D%7BZY%7D%3D%5Cdfrac%7B60%7D%7B48%7D%3D1.25%5C%5C%5C%5C%5Cdfrac%7BUV%7D%7BXY%7D%3D%5Cdfrac%7B50%7D%7B40%7D%3D1.25)
The correct option is A.
Equation is y = -1/6x
Step-by-step explanation:
- Step 1: Given that slope, m = -1/6 and a coordinate (12,-2). Write the equation and find the y-intercept, b.
⇒ y = mx + b
⇒ -2 = -1/6 × 12 + b
⇒ -2 = -2 + b
∴ b = 0
- Step 2: Write the equation in slope intercept form.
⇒ y = -1/6x + 0
⇒ y = -1/6x