What is the approximate perimeter of this triangle?
Understand the Problem
The question is asking for the approximate perimeter of a triangle formed by three coordinate points after Jasmine moves her piece along a grid. We need to calculate the distances between the points and then sum them up to find the perimeter.
Answer
The approximate perimeter of the triangle is $28$ units.
Answer for screen readers
The approximate perimeter of the triangle is $28$ units.
Steps to Solve
- Identify the Coordinates
The coordinates of the points forming the triangle are:
- Point A: $(-2, -4)$
- Point B: $(-1, 6)$
- Point C: $(3, 8)$
- Calculate Distances Between Points
Use the distance formula to calculate the lengths of the sides of the triangle:
The distance formula is given by:
$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$
-
Distance AB:
$$ d_{AB} = \sqrt{((-1) - (-2))^2 + (6 - (-4))^2} = \sqrt{(1)^2 + (10)^2} = \sqrt{1 + 100} = \sqrt{101} \approx 10.05 $$ -
Distance BC:
$$ d_{BC} = \sqrt{(3 - (-1))^2 + (8 - 6)^2} = \sqrt{(4)^2 + (2)^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47 $$ -
Distance CA:
$$ d_{CA} = \sqrt{((-2) - 3)^2 + ((-4) - 8)^2} = \sqrt{(-5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 $$
- Calculate the Perimeter
Sum the lengths of all sides to find the perimeter:
$$ \text{Perimeter} = d_{AB} + d_{BC} + d_{CA} \approx 10.05 + 4.47 + 13 = 27.52 $$
- Round to Approximate Answer
Round the perimeter to the nearest whole number:
The perimeter is approximately $28$ units.
The approximate perimeter of the triangle is $28$ units.
More Information
The perimeter of a triangle is determined by summing the lengths of all its sides. In this problem, we used the distance formula based on the coordinates of the points to find these lengths.
Tips
- Misapplying the distance formula: Ensure you're subtracting the correct coordinates.
- Forgetting to square the differences: Always square the differences inside the square root when using the distance formula.
- Not rounding the final value when approximating the perimeter.
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