Consider the letters of the word. Which letter has no lines of symmetry? A C T N
1 answer:
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The given equations are as follows
(1) First, multiply both sides of equation A by 4, we have
Then, rewrite the left-hand side of the above equation by using the distributive property, we have
This is the required equation B.
In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.
Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.
(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.
As both the equations are the same, so both will have the same solution.
Yes, they have the same solution.
Answer:
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 = -1
- When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5
Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).