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Answer:
Step-by-step explanation:
Given: The triangle with coordinate A(4,6), B(2,-2) and C(-2,-4). D is the mid point of AB and E is the mid point of AC.
To prove: DE is parallel to BC.
Construction: Join DE.
Proof: If we prove the basic proportionality theorem that is , then it proves that DE is parallel to BC.
Now, Mid Point D has coordinates= and Mid Point E has coordinates=
Now, AD=
DB=
AE=
EC=
Now,
=
Hence,
Thus, By basic proportionality theorem, DE is parallel to BC.
Answer:
Step-by-step explanation:
Given an hyperbola with the following conditions:
- Foci at (-10,0) and (10,0)
- x-intercept +/- 6;
The following holds:
- The center is midway between the foci, so the center must be at (h, k) = (0, 0).
- The foci are 10 units to either side of the center, so c = 10 and
- The center lies on the origin, so the two x-intercepts must then also be the hyperbola's vertices.
Since the intercepts are 6 units to either side of the center, then a = 6 and
Therefore, substituting and
into the standard form