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Dafna1 [17]
3 years ago
15

(a) Draw the image of PQR after a rotation of 180° about the origin. Label the image P'Q'R' .

Mathematics
2 answers:
Vilka [71]3 years ago
3 0
A - when doing a 180 degree rotation, the coordinates (x,y) would become (-x,-y), in other words, the inverse of the numbers in the x and y places, (-1,2)->(1,-2)
B - when reflecting over the x axis, only the y coordinate inverts, (x,y) becomes (x,-y), (1,-2)->(1,2)
Strike441 [17]3 years ago
3 0

Answer:

Reflection states that it is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.

(a)

The coordinates of triangle PQR from the given figure is:

P = (1, -1)

Q = (3 , -2)

R = (3 , -4)

To rotate a figure 180 degrees:

The rule of rotation of 180 degree :

(x, y) \rightarrow (-x , -y)

Apply the above rule on PQR we have;

P(1, -1) \rightarrow P'(1 , -1)

Q(3, -2) \rightarrow Q'(2 , -3) and

R(3, -4) \rightarrow R'(4 , -3)

The label of image P'Q'R' as shown below in the figure:

(b)

The rule of reflection across the x-axis is:

(x , y) \rightarrow (x , -y)

Apply the above rule on PQR triangle we get;

P(1, -1) \rightarrow P''(1 , 1)

Q(3, -2) \rightarrow Q''(3, 2)

R(3, -4) \rightarrow R''(3 , 4)

Label of image P"Q"R" as shown in the figure.

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Answer: The time at which the distance between the two is 150 miles is 1.3 hr.

Step-by-step explanation:

Step 1: Sketch the problem as shown in the attached image.

The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.

It follows the equation x² + y² = 15².

The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.

Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>

Which by cross-multiplying gives <em>distance = speed × time</em>.

Let time taken to cover the distance be <em>t h</em>.

Given that Speed of Erin is 9 mph and that of Greg is 7 mph.

Hence, distance covered by Greg, x = 7 × t = 7t.

Distance covered by Erin, y = 9 × t = 9t.

Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>

(7t)² + (9t)² = 15²

49t² + 81t² = 225

(49 + 81)t² = 225

      t² = 225/(49 + 81)

      t² = 225/130

      t² = 1.730769231

       t = √1.730769231

       t = 1.315587029

t = 1.3hr

Hence the time at which the distance between the two is 150 miles is 1.3 hr.

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3 years ago
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