Finding the x-Intercept of a Perpendicular Line Passing Through a Given Point

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Homework Help Overview

The problem involves finding the x-intercept of a line that is perpendicular to another line and passes through a specified point. The context includes concepts from coordinate geometry, specifically dealing with slopes and intercepts.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of slopes and the formation of equations for the lines involved. There is an attempt to combine the equations of two lines, which leads to confusion about the original question regarding the x-intercept.

Discussion Status

The discussion is active, with participants clarifying misunderstandings about the problem requirements. Some guidance has been offered regarding the correct approach to finding the x-intercept, and there are ongoing corrections to earlier calculations.

Contextual Notes

There are indications of mistakes in the calculations presented, particularly in the formulation of the line equations. Participants are also reflecting on the implications of combining the equations, which diverges from the original task.

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Homework Statement



Find the x-intercept of the line that passes through the point (1; 2) and perpendicular to the
line joining (1; 1) and (3; 4):



The Attempt at a Solution



I want to confirm my steps if it's right ,,,,

M=(4-1)/(3-1)= 3/2

y-1=3/2(x-1) ====> y=(3/2)x-1/2

perpendicular = m1xm2=-1 ====> m2=-2/3

y-2=-2/3(x-1) ====> y=(-2/3)x+4/5


making it one equation

(3/2)x-(1/2)=(2/3)x+(4/3)
x=11/13
 
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MrNeWBiE said:
making it one equation

(3/2)x-(1/2)=(2/3)x+(4/3)
x=11/13

I am not sure what you did here. I am assuming you were trying to combine the equation of the first line with the second line. If so, you have calculated the point of intersection of the two lines, which is not what the question has asked for. The question asked you for the x-intercept of the line.
 
aha ,,,
so I should not combine them ,,,

(-2/3)x+4/5 = 0 ?

and the answer will be (10/13,0)
 
Looks good to me!
 
ops ,,,
I had a mistake in y=(-2/3)x+4/5 ,,, should be y=(-2/3)x+8/3

the answer is (4,0) ,,,

btw the for your helping
 

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