Question

Find the lengths of the medians of a Triangle ABC whose vertices are A(8, –8), B(6, 8) C(2, 4).

Answer 1

Step-by-step explanation:

mid point of (6,8) &(2,4)

is ( 4,6)

so length between 2 points (8,-8) & (4,6)

is squere root of 212

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Answer 2

Concept:

The x-axis (horizontal line) and the y-axis (vertical axis) are two perpendicular axes that divide the number line, often referred to as a Cartesian plane, into four quadrants (vertical line).

The graph below shows the four quadrants together with their respective values.

(1st quadrant) (+x, +y)

Second quadrant: (-x, +y)

Quadrant 3 : (-x, -y)

Quadrant 4 : (+x, -y)

The origin is the place where the axes come together. A pair of numbers (x, y) that describe a point's location on a plane are known as its coordinates.

Given:

A(8, –8), B(6, 8) C(2, 4).

Find:

Find the lengths of the medians of a Triangle ABC

Solution:

1) Mid point of (6,8) &(2,4) is ( 4,6)

so length between 2 points (8,-8) & (4,6)

Distance (d) = √(4 - 8)² + (6 - -8)²

= √(-4)² + (14)²

= √212

= 2√53

= 14.560219778561

2) mid point of (8,-8) &(2,4)

is ( 5,2)

so length between 2 points (5,2) & (6,8)

Distance (d) = √(6 - 5)² + (8 - 2)²

= √(1)² + (6)²

= √37

= 6.0827625302982

3) mid point of (6,8) &(8,-8)

is ( 7,0)

so length between 2 points (7,0) & (2,4)

Distance (d) = √(2 - 7)² + (4 - 0)²

= √(-5)² + (4)²

= √41

= 6.4031242374328

Therefore, the lengths of the medians are 14.56, 6.08 and 6.40

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