Which type of triangle is formed with the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices?

Answers

Answer 1

Answer: We will have to use the distance formula in order to determine the lengths of each side of the triangle.

Distance formula: $\sqrt{(x_(2) - x_(1))^(2) + (y_(2) - y_(1))^(2) }$

Let's calculate AB first:
A (1, 7) and B (-2, 2)
A: x1 = 1 and y1 = 7
B: x2 = -2 and y2 = 2

so
$\sqrt{(-2 - 1)^(2) + (2 - 7)^(2) }$
$\sqrt{(-3)^(2) + (-5)^(2) }$
$√(9 + 25 )$
AB = $√(34)$ or (rounded to the nearest tenth) ≈ 5.8

Now let's do BC:
B: x1 = -2 and y1 = 2
C: x2 = 4 and y2 = 2

So
$\sqrt{(4 - -2)^(2) + (2 - 2)^(2) }$
$\sqrt{(6)^(2) + (0)^(2) }$
BC = $√(36 )$ or 6

Now let's do CA
C: x1 = 4 and y1 = 2
A: x2 = 1 and y2 = 7

So
$\sqrt{(1 - 4)^(2) + (7 - 2)^(2) }$
$\sqrt{(-3)^(2) + (5)^(2) }$
$√(9 + 25)$
CA = $√(34)$ or (rounded to the nearest tenth) ≈ 5.8

So let's recap:

AB ≈ 5.8
BC = 6
CA ≈ 5.8

So AB and AC are the same length while BC is .2 units longer which means this is an isosceles triangle.

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Answers

Answer:

the answer would be 135 meters

Step-by-step explanation:

If, to scale on a map, 1 centimeter is 3.5 meters, them 2 centimeters is 7 meters. so on and so forth until 30. 30 (centimeters) times 3.5 (meters) is 135. hope this helped!!!!! reply if this doesn't make sense

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