The steps on the construction of a segment bisector by paper folding, and label the midpoint M is given below.
<h3>What are the steps of this construction?</h3>
1. First, one need to open a Compass so that it is said to be more than half the length of the said segment.
2. Without altering it, with the aid of the compass, do draw an art above and also below the said line segment from one of the segment endpoints.
3. Also without altering it and with use the compass, do draw another pair of arts from the other and points. One arc will be seen above the segment and the other or the second arc will be seen below.
4. Then do draw the point of intersection that is said to exist between the pair of arts below the line segment and also in-between the pair of arts as seen below the line segment
5. Lastly, do make use of a straight edge to link the intersection points between the both pair of arts.
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Given:
- The product of two numbers is (-9/16).
- One of the numbers is (-4/15)
To find: The other number.
Answer:
Let's assume the unknown number to be 'x'.
(-4/15) × x = (-9/16)
× = (-9/16) ÷ (-4/15)
When we divide a fraction by another fraction, the divisor will be taken in its reciprocal form.
x = (-9/16) × (-15/4)
x = 135/64
Therefore, the other number is 135/64.
Hope it helps. :)
Answer:
![x^2 + 4x + y^2 +8y = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%204x%20%2B%20y%5E2%20%2B8y%20%20%3D%20%200)
Step-by-step explanation:
Given
![A = (-1,-2)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C-2%29)
![B = (2,4)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C4%29)
![AP:BP = 1 : 2](https://tex.z-dn.net/?f=AP%3ABP%20%3D%201%20%3A%202)
Required
The locus of P
![AP:BP = 1 : 2](https://tex.z-dn.net/?f=AP%3ABP%20%3D%201%20%3A%202)
Express as fraction
![\frac{AP}{BP} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BAP%7D%7BBP%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Cross multiply
![2AP = BP](https://tex.z-dn.net/?f=2AP%20%3D%20BP)
Calculate AP and BP using the following distance formula:
![d = \sqrt{(x - x_1)^2 + (y - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x%20-%20x_1%29%5E2%20%2B%20%28y%20-%20y_1%29%5E2%7D)
So, we have:
![2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B%28x%20-%20-1%29%5E2%20%2B%20%28y%20-%20-2%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2%7D)
![2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B%28x%20%2B1%29%5E2%20%2B%20%28y%20%2B2%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2%7D)
Take square of both sides
![4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2](https://tex.z-dn.net/?f=4%20%2A%20%5B%28x%20%2B1%29%5E2%20%2B%20%28y%20%2B2%29%5E2%5D%20%3D%20%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2)
Evaluate all squares
![4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%201%20%2B%20y%5E2%20%2B4y%20%2B%204%5D%20%3D%20x%5E2%20-%204x%20%2B%204%20%2B%20y%5E2%20-%208y%20%2B%2016)
Collect and evaluate like terms
![4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%20y%5E2%20%2B4y%20%2B%205%5D%20%3D%20x%5E2%20-%204x%20%2B%20y%5E2%20-%208y%20%2B%2020)
Open brackets
![4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20](https://tex.z-dn.net/?f=4x%5E2%20%2B%208x%20%2B%204y%5E2%20%2B16y%20%2B%2020%20%3D%20x%5E2%20-%204x%20%2B%20y%5E2%20-%208y%20%2B%2020)
Collect like terms
![4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0](https://tex.z-dn.net/?f=4x%5E2%20-%20x%5E2%20%2B%208x%20%2B%204x%20%2B%204y%5E2%20-y%5E2%20%2B16y%20%2B%208y%20%20%2B%2020%20-%2020%20%3D%20%200)
![3x^2 + 12x + 3y^2 +24y = 0](https://tex.z-dn.net/?f=3x%5E2%20%2B%2012x%20%2B%203y%5E2%20%2B24y%20%20%3D%20%200)
Divide through by 3
![x^2 + 4x + y^2 +8y = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%204x%20%2B%20y%5E2%20%2B8y%20%20%3D%20%200)