What is the equation of the line that passes through the origin and is perpendicular to the line that passes through the following points: #(3,7),(5,8)#?

2 Answers
Jun 29, 2018

Answer:

#y=-2x#

Explanation:

First of all, we need to find the gradient of the line passing through #(3,7)# and #(5,8)#

#"gradient"=(8-7)/(5-3)#

#"gradient"=1/2#

Now since the new line is PERPENDICULAR to the line passing through the 2 points, we can use this equation

#m_1m_2=-1# where the gradients of two different lines when multiplied should equal to #-1# if the lines are perpendicular to one another ie at right angles .

hence, your new line would have a gradient of #1/2m_2=-1#
#m_2=-2#

Now, we can use the point gradient formula to find your equation of the line
#y-0=-2(x-0)#
#y=-2x#

Jun 29, 2018

Answer:

Equation of the passing through the origin and having slope = -2 is

#color(blue)(y = -2x " or " 2x + y = 0#

Explanation:

#A (3,7), B(5,8)#

#"Slope of line AB " = m = (y_b - y_a) / (x_b - x_a) = (8-7) / (5-3) = 1/2#

Slope of the perpendicular line = -1/m = -2#

Equation of the passing through the origin and having slope = -2 is

#(y - 0) = -2 (x - 0)#

#color(blue)(y = -2x " or " 2x + y = 0#

graph{-2x [-10, 10, -5, 5]}