0
Solution (A):
Since the line segment start at origin (0, 0) and ends at (0, 4) it lies on the y-axis. So we can say that the midpoint of that line segment is (0, 2).
Since the line segment with length 4 is one of the sides of the equilateral triangle, and the lines where the two other sides of the triangle, also of length 4, lie on the first quadrant, their point of the intersection (x, y) would be the third vertex [two other vertices are (0, 0) and (0,4)].
Since in an equilateral triangle the median is also an altitude , then the line that passes through the midpoint (0, 2) and the vertex (x, y) is parallel to the x-axis. Since this horizontal line has an equation y = 2, then the y-coordinate of the third vertex would be 2; (x, 2).
The median or altitude separates the equilateral triangle into two right triangles with base length 2 and hypotenuse length 4.
From the Pythagorean Theorem, the altitude length would be 2√3 [√(42 - 22) = √12).
If from the vertex (x, y),we draw a line perpendicular to the x-axis, it intersects the x-axis at x = 2√3 (since the distance of two parallel lines intersected by two perpendicular lines, to them, is the same). Since this vertital line has an equation x = 2√3, then the x-coordinate of the third vertex would be 2√3.Thus, we can say that the third vertex would be (2√3, 2).
Or you can work using the distance formula, such as:
Since the line segment start at origin (0, 0) and ends at (0, 4) it lies on the y-axis.
Since the line segment with length 4 is one of the sides of the equilateral triangle, and the lines where the two other sides of the triangle, also of length 4, lie on the first quadrant, their point of the intersection (x, y) would be the third vertex [two other vertices are (0, 0) and (0,4)].
We know that:
the distance between the points (x, y) and (0, 0) is 4, and also
the distance between the points (x, y) and (0, 4) is 4.
By using the distance formula we have:
√[(x - 0)2 + (y - 0)2] = 4, and
√[(x - 0)2 + (y - 4)2] = 4
So that:
√[(x - 0)2 + (y - 0)2] = √[(x - 0)2 + (y - 4)2] square both sides;
x2 + y2 = x2 + y2 - 8y + 16
.
.
y = 2
Substituting 2 for y into the one of the distance formula above, we find x = 2√3
So that the third vertex would be (2√3, 2). Solution (B): The slope of the line that passes through (0, 0) and (2√3, 2) is √3. (2√3 - 0)/(2 - 0) = (2√3)/2 = √3 The slope of the line that passes through (0, 4) and (2√3, 2) is -√3. (2√3 - 0)/(2 - 4) = (2√3)/-2 = -√3
What else can I help you with?
Does a equiangular triangle have to be equilateral?
No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral
Are isosceles triangle sometimes an equilateral triangle?
Are isosceles triangle sometimes an equilateral triangle
What triangle has all the angles the same measures?
The equilateral triangle.
What types of faces are found in an equilateral triangle?
One face that is the equilateral triangle.One face that is the equilateral triangle.One face that is the equilateral triangle.One face that is the equilateral triangle.
Why is an equilateral triangle called equilateral triangle?
all the sides are equal
Does a equiangular triangle have to be equilateral?
No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral
How is a triangle the same as a equilateral triangle?
A triangle is the same as a equilateral triangle because a equilateral triangle is a triangle but it is congruent on all sides
What is an equilateral triangle obtuse triangle?
An oxymoron. An equilateral triangle cannot be obtuse; an obtuse triangle cannot be equilateral.
What kind of shape is an equilateral triangle?
there is not one because a equilateral triangle is one triangle so the ansew is equilateral triangle
Are isosceles triangle sometimes an equilateral triangle?
Are isosceles triangle sometimes an equilateral triangle
What triangle has all the angles the same measures?
The equilateral triangle.
What is a 4cm by 4cm by 4cm triangle called?
It is an equilateral triangle
What types of faces are found in an equilateral triangle?
One face that is the equilateral triangle.One face that is the equilateral triangle.One face that is the equilateral triangle.One face that is the equilateral triangle.
Is an equilateral triangle be an obtuse triangle?
No, an equilateral triangle can not be an obtuse triangle. All angles in an equilateral triangle are 60o. An obtuse triangle has 1 angle that is greater than 90o.
Can A equilateral triangle can be a cute?
No, but an equilateral triangle must be acute.
What is a real life example of an equilateral triangle?
An equilateral triangle is a triangle in which all three sides are equal. The yield sign on highways is an equilateral triangle.
A triangle with all sides the same length?
is called an equilateral triangle
