Answer:
Length = 15
Width = 6
Area = 90
Step-by-step explanation:
Area of the rectangle =
Lets factorise the polynomial
We know that Area = Length × Width
Let the length be (x + 3) & width be (x - 6)
Its given in the question that x = 12. So putting the value of x gives ,
Length =
Width =
Area = Length × Width = 15 × 6 = 90
Transformations in the coordinate plane maps preimage coordinate points to the coordinate points of the image
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The reason the above values are correct are as follows:
The given parameter are;
The coordinates of Emma's initial triangle are; (3, 0), (-4, -2), (-2, -2)
Tony's initial triangle coordinates are; (2, 4), (2, 2), (4, 3)
The vector used on the first turn is <6, -5>, which gives;
Emma's first transformation,
1st quadrant (3, 0) → 4th quadrant (9, -5)
3rd quadrant (-4, -2) → 4th quadrant (2, -7)
3rd quadrant (-2, -2) → 4th quadrant (4, -5)
Tony's first transformation,
1st quadrant (2, 4) → 4th quadrant (8, -1)
1st quadrant (2, 2) → 4th quadrant (8, -3)
1st quadrant (4, 3) → 4th quadrant (10, -2)
Emma's second transformation,
4th quadrant (9, -5) → 2nd quadrant (-1, 3)
4th quadrant (2, -7) → 2nd quadrant (-8, 1)
4th quadrant (4, -5) → 2nd quadrant (-6, 3)
Tony's second transformation,
4th quadrant (8, -1) → 2nd quadrant (-2, 7)
4th quadrant (8, -3) → 2nd quadrant (-2, 5)
4th quadrant (10, -2) → 1st quadrant (0, 6)
From the above translation transformations, Emma has drawn an image in the 4th and 2nd quadrant, and would needs to draw an image in the <u>3rd and 1st quadrant </u>
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Similarly, from the above values, Tony has drawn an image in the 4th quadrant, 2nd quadrant and 1st quadrant, therefore Tony needs to translate to only the <u>3rd quadrant </u>in order to win
Learn more about transformations in the coordinate plane here: