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Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.

1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.

2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).


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Sagot :

The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).

What is transformation in math?  

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.

The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:

  • Translation
  • Rotation
  • Reflection; and
  • Dilation.

What transformations would you use on the blue triangle to get it to match with the red triangle?

The type of transformation that will be used here is called reflection.

D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).

Which line segments on the boat are parallel?

The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).

Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.

Which line segments on the boat are perpendicular?

The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.

Which line segments on the boat have a slope of 0?

The line segments on the boat that have a slope of zero are:
EF, AB AC, BC.  A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.

Which line segments on the boat have an undefined slope?

The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.

What is the slope of ED?

The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)

Given that:

Y1 = 5

Y2 = 4

X1 = -10

X2 = -11

Hence,
m = (5-4)/(-11 -10)

m = -0.048

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