Geometry, SEMI-EASY question. I will give brainliest. Just want to double-check.
1 answer:
Answer:
Option B
Step-by-step explanation:
Let the point O is the origin.
Then the coordinates of the vertices A,B and C will be,
A → (-12, -8)
B → (-8, 0)
C → (-6, -4)
Rule for the dilation of a point (x, y) by scale factor 'k' about the origin is,
(x, y) → (kx, ky)
By this rule, coordinates of the vertices of the image triangle will be,
If k = ,
A(-12, -8) → A'(-6, -4)
B(-8, 0) → B'(-4, 0)
C(-6, -4) → C'(-3, -2)
From the given options,
Option B is the answer.
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The value of d is -2
Step-by-step explanation:
The nth term of the arithmetic sequence is , where
is the first term
- d is the common difference between each 2 consecutive terms
The nth term of the geometric sequence is , where
- r is the common ratio between each two consecutive terms
∵ of an arithmetic sequence is 1
∵ The common difference is d, where d ≠ 0
∵ ,
,
are the first 3 terms of a geometric sequence
∵ = 1 + (2 - 1)d
∴ = 1 + d
∵ = 1 + (3 - 1)d
∴ = 1 + 2d
∵ = 1 + (6 - 1)d
∴ = 1 + 5d
∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,
(1 + 5d)
∵ The common ratio in the geometric sequence is
∴
- Use cross multiplication with the equal fractions
∵
∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)
∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²
- Add like terms in each side
∴ 1 + 4d + 4d² = 1 + 6d + 5d²
- Subtract 1 from both sides
∴ 4d + 4d² = 6d + 5d²
- Subtract 4d from both sides
∴ 4d² = 2d + 5d²
- Subtract 4d² from each side
∴ 0 = 2d + d²
- Take d as a common factor
∴ 0 = d(2 + d)
- Equate each factor by 0
∴ d = 0 but we will reject it because d ≠ 0
∴ 2 + d = 0
- Subtract 2 from both sides
∴ d = -2
The value of d is -2
Learn more:
You can learn more about the sequence in brainly.com/question/1522572
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