The midpoint of overline AB is M(7,-7) . If the coordinates of A are (8, - 6) , what are the coordinates of B?

1 answer:

5 0

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.

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Which graph shows the result of dilating this figure by a factor of 4 about the origin? On a coordinate plane, rectangle A B C D

Andrei [34K]

Answer:

Second option: On a coordinate plane, rectangle A'B'C'D' prime has points $(-4,4),(12,4),(12,-4),(-4,-4)$

(See the graph attached)

Step-by-step explanation:

For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.

In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

$A(-1,1)\\\\B(3,1)\\\\C(3,-1)\\\\D(-1,-1)$

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

$A'=((-1)(4),(1)(4))=(-4,4)\\\\B'=((3)(4),(1)(4))=(12,4)\\\\C'=((3)(4),(-1)(4))=(12,-4)\\\\D'=((-1)(4),(-1)(4))=(-4,-4)$