![02lesmun16219](/avatars/22764.jpg)
02lesmun16219
24.06.2021 •
Mathematics
The coordinates of AB are A(2,3) and B(8,1) The perpendicular bisected of AB is CD and point C lies on AB the length of CD is 10 units
Solved
Show answers
More tips
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
- C Computers and Internet Which Phone is Best for Internet Surfing?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- C Computers and Internet How to Learn to Type Fast?...
Answers on questions: Mathematics
- M Mathematics Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises. use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises. use the function f(x) = 2x3 - 3x2 + 7 to...
- M Mathematics Lin parachutes from a plane at a height of 22,000 ft above sea level. several minutes later she notes from an instrument on her wrist that she had dropped 10,000 ft. how...
- M Mathematics Y=x+2 and then you have x=-3 you also have to use transitive property...
- M Mathematics Jeremy saves $35 per month over the first 7 months of the year. he saves $40 per month over the next 5 months of the year. if jeremy spends none of his savings, which expression...
- M Mathematics On a graph with y-values ranging from 818 to 1012, what is a reasonable scale to use on a y-axis with 20 tick marks...
- M Mathematics Simplify the expression: ((xy^-2)^3)/((y^3)(x^-2))^1/3...
- M Mathematics Write an equation that is linear but not standard form...
- M Mathematics Which list is ordered from least to greatest? a. –5, –2.1, 0.3, 3.1 b. 0.3, –2.1, 3.1, –5 c. –2.1, –5, 0.3, 3.1 d. 0.3, 3.1, –2.1, –5...
- M Mathematics Choose the correct word to complete the following sentance: a natural number is (always, sometimes, never) a whole number...
- M Mathematics Perform the indicated operation. 2/3 - 5/8 1. 5/12 2. 5/6 3. 1/24...
Ответ:
The Coordinates of Point C are C(5,2)
The slope of CD is 3
The possible coordinates of point D(a,b) are (6, 5) and (4, -1)
Step-by-step explanation:
According to the Question,
Given, The end points of AB are A(2,3) and B(8,1). The perpendicular Bisector of AB is CD, and point C lies on AB. The length of the CD is √10 units.Now, Let The Coordinates of Point C are C( x , y ) .
Thus, C( x , y ) =The Coordinates of Point C are C( x , y ) =
⇒C(5, 2).
And, The slope of AB =Thus, The slope of CD is
=
⇔ 3.
Let the coordinate of D be (a, b) then⇒ √{ (b - 2)² +(a - 5)² } = √10
on squaring both sides we get,
⇒ a² - 10a + 25 + b² - 4b + 4 = 10
⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)
We Know, the slope of CD = 3⇒Thus, (b - 2)/(a - 5) = 3
⇒ b - 2 = 3a - 15
⇒ b = 3a - 13 ⇔⇔ (Equation 2)
Putting value of Equation 2 into Equation 1, We get⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19
⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19
⇒10a² - 100a + 240 = 0
⇒a² - 10a + 24 = 0
⇒(a - 4)(a - 6) = 0
⇒a = 4 or a = 6
Now,
When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).
Ответ:
Step-by-step explanation:
We are given a
where ![\angle K = 90^\circ](/tpl/images/0696/2151/ca839.png)
As per trigonometric rules,
Comparing the given value of tangent and cosine:
Perpendicular = 3 units
Base = 4 units
Hypotenuse = 5 units
Also, we know that:
Now, it is given that the triangle is dilated by a scale factor of
.
i.e. all the sides will become half of its initial values.
New Perpendicular = 1.5 units
New Base = 2 units
New Hypotenuse = 2.5 units
Using the formula for sine: