Answer:
see below for drawings and description
Step-by-step explanation:
For geometry problems involving translation, rotation, and reflection—transformations that change location, but not size ("rigid" transformations)—it might be helpful for you to trace the image onto tracing paper or clear plastic so that you can manipulate it in the desired way. Eventually, you'll be able to do this mentally, without the aid of a physical object to play with.
For the images attached here, I copied the triangle onto a piece of clear plastic so I could move it to the desired positions. The result was photographed for your pleasure.
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a. Translation means the image is moved without changing its orientation or dimensions. You are asked to copy the triangle so that the upper left vertex is moved to what is now point E. See the first attachment.
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b. Reflection means the points are copied to the same distance on the other side of the point or line of reflection. Just as an object held to a mirror has its reflection also at the mirror, any points on the line of reflection do not move. Reflection flips the image over. See the second attachment.
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c. Rotation about point D means point D stays where it is. The angle of rotation is the same as the angle at D, so the line DE gets rotated until it aligns with the line DF. The rest of the triangle maintains its shape. See the third attachment.
Answer:
1.5.80 miles
2.9.80ft
3.56 inches
4.5.20 units
5. 13 units
6.5.40 ft
Step-by-step explanation:
⇒These questions are on the Pythagorean relationship
⇒General expression is ;
a²+b²=c² where a and b are values for the legs and c is the hypotenuse
1. Isaiah waked 3 miles north and 5 miles east.
Finding the distance from starting point we apply the equation;
a²+b²=c² where a=5 miles and b=3miles
5²+3²=c²
25+9=c²
34=c²
c=√34 = 5.80 miles
2.The ladder is leaning against the wall to form the hypotenuse side of 10 ft.The distance from the base to the ladder forms side a= 2ft. The question requires you to calculate the height b.
a²+b²=c²
2²+b²=10²
4+b²=100
b²=100-4
b=√96
b=9.80 ft
3. The television has a diagonal of 70 inches to represent side c and a height of 42 inches to represent the side a. The question requires you to find the width of the television which represents the side b
a²+ b²=c²
42²+b²=70²
b²=70²-42²
b=√3136
c=56 inches
4. An equilateral triangle is one that has all its sides and angles equal. Here you have to introduce a perpendicular line from the apex point of the triangle to the base and get the distance a.The using the hypotenuse and the distance a, you can find the height/b.
c= 6 units and a=6/2= 3 units
a²+b²=c² 3²+ b²= 6²
9+b²=36
b²=36-9
b=√27 =5.20 units
5.In this question, you are given the height and the width of the right triangle thus apply the relationship as;
a²+b²=c²..........where a=5 and b=12
5²+12²=c²
25+144=c²⇒⇒⇒c=√169 =13 units
6. In this question, the height of the plant represents side b and the distance of the base from where the string is tied is side b.You are to find the length of the string which represents the hypotenuse side.
a²+b²=c²
5²+2²=c²
25+4=c²
29=c²
√29=c
c=5.40 ft
Explanation:
It helps to understand the process of multiplying the binomials. Consider the simple case ...
(x +a)(x +b)
The product is ...
(x +a)(x +b) = x² +(a+b)x + ab
If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.
If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).
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Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.
<u>Example</u>:
x² -x -6
-6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.
-6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)
The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.
x² -x -6 = (x -3)(x +2)
Remember that moving on the x axis is 1 and on the y axis 2
