Question

Line FG goes through the points (4,9) and (1,3). Which equation represents a line that is perpendicular to FG and passes through the point (2,0)?
-2x+ y=-4
-2x+y=2
X+2y=2
X+2y=4

Answer 1

Answer:

$x + 2y= 2$

Step-by-step explanation:

Given

Points:

$F = (4,9)$

$G = (1,3)$

Required

Determine the equation of line that is perpendicular to the given points and that pass through $(2,0)$

First, we need to determine the slope, m of FG

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$F = (4,9)$ --- $(x_1,y_1)$

$G = (1,3)$ --- $(x_2,y_2)$

$m = \frac{3 - 9}{1 - 4}$

$m = \frac{- 6}{- 3}$

$m =2$

The question says the line is perpendicular to FG.

Next, we determine the slope (m2) of the perpendicular line using:

$m_2 = -\frac{1}{m}$

$m_2 = -\frac{1}{2}$

The equation of the line is then calculated as:

$y - y_1 = m_2(x - x_1)$

Where

$m_2 = -\frac{1}{2}$

$(x_1,y_1) = (2,0)$

$y - 0 = -\frac{1}{2}(x - 2)$

$y = -\frac{1}{2}(x - 2)$

$y = -\frac{1}{2}x + 1$

Multiply through by 2

$2y = -x + 2$

Add x to both sides

$x + 2y= -x +x+ 2$

$x + 2y= 2$

Hence, the line of the equation is $x + 2y= 2$

Answer 2

Answer:

X+2y=2

Step-by-step explanation: