1) Slope of diagonal GE: 3
2) Equation of the line:
3) Slope of the line: 1
4) y-intercept: 4
Step-by-step explanation:
1)
Here the diagonal FH is given by the line with equation
This line is written in the form
where m is the slope of the line and are the coordinates of a point on the line.
Therefore, for line FH we have:
(slope)
Diagonal GE is perpendicular to diagonal FH (the diagonals in a square are perpendicular): this means that its slope must be equal to the inverse reciprocal of the slope of FH. THerefore, the slope of diagonal GE is
2)
Two lines are said to be parallel when they have same slope.
Here, we see that the line given in the plot passes through the points
Therefore the slope of the line shown is
This means that also the line that we want to find must have slope of 1:
Now we can use the following form to write the equation of this line:
where:
is the point that must be on the line
Therefore,
3)
In order to solve this problem, we have to find the slope of the side WV.
The coordinates of the two points are:
Therefore, the slope of side WV is given by:
And we said that two lines are parallel if they have same slope: therefore, the slope of the line parallel to the line that contains side VW is also 1.
4)
The line given in this problem has equation:
where
is the slope of the line
is the y-intercept of the line
Here we want to find the line perpendicular to the given line and passing through the point (4,1).
A line perpendicular to the given one must have a slope which is equal to the negative of the reciprocal of the original one, therefore:
Now we can use the form
and the coordinates of the point are
Substituting,
We have written the line in the form , with
: so the y-intercept is 4.
Learn more about parallel and perpendicular lines:
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