Find the length of a segment with endpoints at (1,-2) and (-4,-4)

Mathematics

1 answer:

Paha777 [63]3 years ago

6 0

Call $(1,-2)$ for point A and $(-4, -4)$ for point B

Use the distance formula $AB = d(A, B) = \sqrt{(x_{B} - x_{A})^2 + (y_{B} - y_{A})^2}$

Insert values for $x_{B}$ , $x_{A}$ , $y_{B}$ and $y_{A}$

$AB = \sqrt{(-4 - 1)^2 + (-4 - (-2))^2}\\= \sqrt{(-4 - 1)^2 + (-4 + 2)^2}\\= \sqrt{(-5)^2 + (-2)^2}\\= \sqrt{25 + 4}\\= \sqrt{29}$

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John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground opposite

otez555 [7]

John's method to determine the width of the stream uses the knowledge

that the tangent of 60° is approximately 1.7.

The proper sequence John would use to find the width of the stream are;

Step 1; John drives a stake opposite the tree to establish a line between two points

Step 2; John uses a compass to walk away from the stakes at a right angle

Step 3; On the path John walks until he finds a line of sight to the tree that equals 60 degrees

Step 4; John drives a second stake in the ground

Step 5; John measures the the distance between the two stakes

Step 6; John multiplies the distance between the two stakes by 1.7 to find the distance.

Reasons:

The steps that can be used to measure the width of the stream are;

Step 1: Drive a stake opposite the tree on the other side of the stream.

Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.

Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.

Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.

Step 5; Measure the distance between the stakes that are placed in the ground.

Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.

$\displaystyle tan(60^{\circ}) = \mathbf{\frac{Width \ of \ stream}{Distance \ between \ stakes}}$