185k views
4 votes
You need to find 3 things: The coordinates for M, The Length of the Median AM, The coordinates of the Centroid P. Please explain with answers. a) The coordinates for M are (x₁, y₁), The Length of the Median AM is √((x₁ - x)² + (y₁ - y)²), The coordinates of the Centroid P are (x, y). b) The coordinates for M are (x, y), The Length of the Median AM is √((x - x₁)² + (y - y₁)²), The coordinates of the Centroid P are (x₁, y₁). c) The coordinates for M are (x, y), The Length of the Median AM is √((x - x₁)² + (y - y₁)²), The coordinates of the Centroid P are (x, y). d) The coordinates for M are (x₁, y₁), The Length of the Median AM is √((x - x₁)² + (y - y₁)²), The coordinates of the Centroid P are (x₁, y₁).

User Zach Jensz
by
7.6k points

1 Answer

2 votes

The correct answer is b). Let me explain:

The centroid (P) of a triangle is calculated using the formula:

P = 1/3 * (x₁, y₁)

This is basically the average of the coordinates of the three vertices of the triangle.

The mid-point (M) is calculated by taking the average of the x-coordinates and y-coordinates of the three vertices of the triangle. That is:

M = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3

This forms the coordinates for M which is (x, y).

Next, the length of the median (AM) from the vertex A to the mid-point M is calculated using the distance formula:

AM = sqrt((xM - xA)² + (yM - yA)²)

That is, AM = √((x - x₁)² + (y - y₁)²).

So our M is (x, y), AM is √((x - x₁)² + (y - y₁)²), and P is (x₁, y₁). This is stated in option b). Therefore, the correct option is b).

User ArinCool
by
9.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories