The next term of the series, 3, 10, 29, 66, 127 is 218.
Answer:
The coordinates of the mid-point are :

Step-by-step explanation:
We know that, the coordinates of the mid-point (<em>x</em>, <em>y</em>) of a line segment joining the points (<em>x</em>₁, <em>y</em>₁) and (<em>x</em>₂, <em>y</em>₂) is given by

Now, we have the given points as (3, 5) and (-2, 0).
By using the above formula, coordinates of the mid-point (<em>x</em>, <em>y</em>) of the line-segment joining the points (3, 5) and (-2, 0) is given by,


∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is
.
<h2>
Answer with explanation:</h2>
1)
The vertices of X,Y and Z are:
X(-2, 0), Y(-2, -1), and Z(-5, -2)
Now, when X,Y and Z are translated by using the translation transformation:
(x,y) → (x+6,y-2)
Then we obtain the transformation:
X(-2, 0) → X′(4, -2)
Y(-2, -1) → Y′(4, -3)
Z(-5, -2) → Z′(1, -4)
The type of transformation that triangle XYZ undergoes is a translation transformation by the rule: (x,y) → (x+6,y-2)
2)
Next when we reflect the triangle X'Y'Z' across the x-axis then we obtain X"Y"Z"
Since, the rule that follow on reflecting across x-axis is:
(x,y) → (x,-y)
Hence, we get:
X′(4, -2) → X″(4, 2)
Y′(4, -3) → Y″(4, 3)
Z′(1, -4) → Z″(1, 4)
Hence, the type of transformation that triangle X′Y′Z′ undergoes is a reflection transformation (on reflecting across x-axis)
Answer:

Step-by-step explanation:
This is the answer because it is subtracted so that you get the answer