Question

4. A triangle has vertices A(4, 2), B(3, 7), and C(–4, –5).

Answer 1

To draw the median of the triangle from vertex A, the mid point of BC must be determined. The median of the vertex A is given at (-1/2, 1). See explanation below.

How you would draw the median of the triangle from vertex A?

Recall that B = (3, 7)

and            C = (-4, -5).

• Note that when you are given coordinates in the format above, B or C = (x, y)
• Hence the mid point of line BC is point D₁ which is derived as:
  D₁ $[ (\frac{3-4}{2})$ , $(\frac{7-5}{2}) ]$
• hence, the Median of the Vertex A = (-1/2, 1).

Connecting D' and A gives us the median of the vertex A. See attached graph.

What is the length of the median from C to AB?

Recall that
A → (4, 2); and

B → (3, 7)

Hence, the Midpoint will be

$[(\frac{4+3}{2} )$, $(\frac{2+7}{2} )]$

→  $(\frac{7}{2}, \frac{9}{2} )$

Recall that

C → (-4, 5)

Hence,

$\overline{C D_{2} }$ =  $\sqrt{[(-4 -\frac{7}{2} })^{2} + (-5-\frac{9}{2} )^{2} ]$

Simplified, the above becomes

= √(586)/2)

= 24.2074/2

= 12.1037

The length of the Median from C to AB ≈ 12

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