Answer:
x = 9
Step-by-step explanation:
Given a segment joining the midpoints of 2 sides of a triangle, then
the segment is half the length of the 3rd side , that is
3x = 0.5 × 54 = 27 ( divide both sides by 3 )
x = 9
The general equation of the line:
y = mx + c
where m is the slope of the line , and c is constant
m will be calculated using the points (2,1162) , (11,1900) as follow
m = (1900-1162)/(11-2) = 82
∴ y = 82 x + c
By substituting with the point (2,1162) to find c
∴ c = y - 82x = 1162 - 82 * 2 = 998
∴ y = 82x + 998
The first choice is the correct answer
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction[switch the numerator and the denominator])
For example:
Slope = 
Perpendicular line's slope =
or -3
Slope = -2 or 
Perpendicular line's slope = 
The given line's slope is
, so the perpendicular line's slope is -3. Now that you know the slope, substitute/plug it into the equation:
y = mx + b
y = -3x + b To find b, plug in the point (1, 9) and isolate/get the variable "b" by itself in the equation
9 = -3(1) + b Add 3 on both sides to get "b" by itself
9 + 3 = -3 + 3 + b
12 = b
y = -3x + 12
30 + 25m = 80 + 15m
25m - 15m = 80 - 30
5m = 50
m = 10