Answer:
Coordinate: (0,15)
Explanation:
To find the equation of the line perpendicular to the line joining (4,1) and (8,3) and passing through the point (6,3), we can follow these steps:
Find the slope of the line joining (4,1) and (8,3).
Slope (m) = (change in y) / (change in x)
Slope (m) = (3 - 1) / (8 - 4)
Slope (m) = 2 / 4
Slope (m) = 1/2
So, the slope of the line joining (4,1) and (8,3) is 1/2.
Now,
Determine the negative reciprocal of the slope.
The negative reciprocal of 1/2 is -2.
Use the point-slope form of a line to find the equation of the perpendicular line.
The point-slope form of a line is given by:
y - y₁ = m(x - x₁)
where:
- (x₁, y₁) is a point on the line (in this case, (6,3)),
- m is the slope of the line (in this case, -2).
Substitute the values:
y - 3 = -2(x - 6)
Simplify this equation:
y - 3 = -2x + 12
Add 3 to both sides to isolate y:
y = -2x + 12 + 3
y = -2x + 15
To find the coordinate take any value of x and substitute it this equation and solve it.
If x = 0,
y = -2 × 0 + 15
y = 15
Therefore, one coordinate is (0,15).
Note:
We can find an infinite number of coordinates by substitution of any value of x in the equation y = -2x + 15.