What is the missing reason in the proof?

Perpendicular bisector theorem

Step-by-step explanation:

Perpendicular bisector theorem: if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.

So, if segment ST is the perpendicular bisector of segment RV, then, by perpendicular bisector theorem, any point in segment ST (like S) is equidistant from points R and V, in consequence, segments RS and SV are equal.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

the answer is y = 11.54

hope this : )