Answer:
y = 3x -1
Step-by-step explanation:
When the given points are dilated by a factor of 1/5 about the origin, each of the coordinate values is multiplied by 1/5. The points after dilation are ...
... (2/5, 1/5), (-1/5, -8/5)
The line through these points can be found starting with a 2-point form of the equation for the line.
... y -y1 = (y2 -y1)/(x2 -x1)·(x -x1)
Filling in the point values gives ...
... y -1/5 = (-8/5 -1/5)/(-1/5 -2/5)(x -2/5)
... y = (-9/5)/(-3/5)(x -2/5) +1/5 . . . . simplify parentheses, add 1/5
... y = 3x -1 . . . . . simplify
_____
The graph shows the original points and the line through them in red, and the dilated points and line in green.
Answer:
∠x = 60°
Step-by-step explanation:
first:
∠a = 60° was given
the sides on each side of ∠a are equal so their opposite angles are equal also.
The sum of the interior angles of any triangle is 180°
The angles opposite ∠a are (180° - 60°)/2 = 60° each
Second:
∠b = 60° was given
so the angles opposite ∠b are also 60° each
Third:
the 2 angles opposite x are both 60° each because they are both vertical angles to 60°
That leaves ∠x to be 180° - 60° - 60° = 60°
Answer:
Area of geometric figures mentioned calculated.
Step-by-step explanation:
Square Perimeter = 4 x sides of square = 20. So, each equal side of square = 20 / 4 = 5
Area of square = ( Side )^2 = ( 5 )^2 = 25
Area of triangle = 1/2 (Base) (Height) = 1/2 x 3 x 3.5 = 5.25
Answer:
the new height of the triangle = 2.449
Step-by-step explanation:
Given that:
the sides of the triangle are 4m in length i.e they are equal. It shows that the triangle is known to be an equilateral triangle.
Let say the triangle is a triangle IJK
Let the length of the side to be i = 4
Definitely
IJ = JK = IK = i = 4
If a midline is drawn and cuts the equilateral triangle in two equal halves of a right-angle triangle. Then, suppose the midline is L
Then ;


Let consider triangle IJL
(IL)² = (IJ)² - (JL)²




Area of triangle IJK can be expressed as:



where, i = 4
Then:



when the area is exactly half of the original triangle's area, the new height is :








Finally, the new height of the new triangle is:




IL = 2.449 m