1) Triangle T1 is transformed into triangle T2 by a. dilation with scale factor of 1/2
b. reflection over the y-axis
c. translation

2) and triangle T2 is transformed into trinagle T3 by
a. dilation with scale factor 1/2
b. reflection over the x-adis
c. rotation

1) The correct option is;

b. Reflection over the y-axis

2) The correct option is;

a. Dilation by a scale factor of 1/2

Step-by-step explanation:

1) The rule for reflection over the y-axis is given as follows;

Given the point of the preimage before the reflection = (x, y), the point of the image after the reflection will be (-x, y)

The coordinate of a point on T1 is (-2, 4). The coordinate of similar point in T2 is (2, 4) which satisfies the rule for reflection over the y-axis

2) The length of a side in triangle T2 is given by the formula for finding the length, l, of segments between coordinate points as follows;

Point 1, (x₁, y₁) = (2, 4)

Point 2, (x₂, y₂) = (6, 2)

The length = √((2 - 4)² + (6 - 2)²) = 2·√5

The length of the corresponding side in T3 is given as follows;

Point 1, (x₁, y₁) = (1, 2)

Point 2, (x₂, y₂) = (3, 1)

The length = √((1 - 2)² + (3 - 1)²) = √5

The length of of a side T3 = 1/2 of the length of a side of T2

Therefore. triangle T2 is transformed into triangle T3 by dilation with a scale factor of 1/2.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

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