Answer:
A
Step-by-step explanation:
To construct the perpendicular bisector, follow these steps:
Step 1:
Set the compass to a distance greater than half the length of segment AB, place it on point A, and draw an arc across AB.
Step 2:
Keeping the same width, place the compass on point B and create another arc across AB.
Step 3:
With the ruler, connect the two intersection points of the arcs by drawing a line.
Step 4:
This line will be the perpendicular bisector of the segment AB.
Thus, option A is the correct choice.
Answer:
1. x=±4
2. t=±9
3. r=±10
4. x=±12
5. s=±5
Step-by-step explanation:
1. x^2 = 16
By extracting the square root on both sides
x=±4
2. t^2=81
Again, take the square root of each side
t=±9
3. r^2-100=0
r=±10
4. x²-144=0
We rewrite as x²=144
Applying square roots
x=±12
5. 2s²=50
s=±5 ..
The characterization of HIJK as a parallelogram arises from the fact that the midpoints of both diagonals coincide at (1, 0), which indicates that these diagonals bisect each other. To explicitly demonstrate this, we determine that the midpoints of the diagonals HJ and IK are equal, confirming HIJK's properties as a parallelogram.
Given the specified angles, one is 90 degrees, indicating that the triangle is a right triangle. With provided angles and one side representing the hypotenuse (the longest side), the area is determined using the formula: Area = 1/2 * base * height. Let's compute the height and base:
From sin 75, we derive height = 1.67.
And from cos 75, we obtain base = 0.45.
Calculating area gives us Area = (0.45 * 1.67) / 2, resulting in 0.37 square units.
Thus, the triangle's area is approximately 0.37 square units.
