Solve the equation for b: A= (1/2)(b)(h)
2 answers:
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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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Answer:
The correct answer is yes, we can draw an isosceles triangle with only one 80° angle. NO this is not the only possibility.
Step-by-step explanation:
A triangle is a three sided figure. There are three types of triangles: Equilateral, Isosceles and Scalene triangle. The sum of angles in a triangle is 180°.
If all sides have equal length then it is an equilateral triangle. All angles of this triangle are equal.
If two sides are equal then it is an isosceles triangle. Two opposite angles are equal.
If none of the angles and sides are equal then we call it a scalene triangle.
Given one angle of the triangle is 80°.
There exists two possibilities. One, 80° is the equal angle and 80° is not the equal angle.
Required Case : 80° is not the equal angle, i.e. only one 80° angle.
We are to draw an isosceles triangle (say ABC) with one angle say ∠A as 80°.
Other two angles (∠B and ∠C) are 50° each as the other two angles are supposed to be equal. (°).
Now let us consider side AB and AC be of length say a. These two sides are equal.
Thus now we have successfully constructed an isosceles triangle with only one 80° angle.
We can get infinitely many isosceles triangle by just varying the length of the equal side.