How do you solve this math problem???

Question

Uhhh how do you start out solving this??? Please explain to me in detail if possible. Thank you.

4. Find the value of x so the line that passes through (x, 5) and (12, 2) is perpendicular to the line that passes through (0, 1) and (2, 7).

Answer 1

Ok..its been a while for me..but I think in order for a line to be perpendicular to another line, the slope has to be the negative reciprocal of the other line's slope. Since the other line's slope is 3 (7-1 divided by 2-0), then the slope of the other line must be
-1/3. So.. (2-5)/(12-x) must = -1/3............ -3/(12-x)= -1/3 Just solve that equation and you have x :)

Hint: X = 3

Answer 2

Start with the line through (0,1) & (2,7):
m = (7-1)/(2-0) = 6/2 = 3.
b = 1, the y-intercept is given: (0,1).
The equation of the line is:
y= 3x + 1.

The slope of the second line, through (x,5) & (12,2), is m = -(1/3); since the lines are perpendicular, m1m2 = -1.
-(1/3) = (2-5)/(12-x)
-(12-x) = 3(-3)
x - 12 = -9
x = -9 + 12
x = 3.

Point-Slope form of this line is:
y - 2 = -(1/3)(x - 12)
y = -(1/3)x + 4 + 2
y = -(1/3)x + 6.

Ck. y = -(1/3)(3) + 6 = 5.
So, (3,5) is the desired point.

Answer 3

Yeah! the above answer is right