Finding original price with 75 percent of discount and $55.50 sale price
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1.
If we are given 2 points A(a, b) and B(c, d),
the midpoint M, of segment AB has coordinates:
2.
We are given the points A(2, 3) and B(10, 3)
the midpoint of AB, is given by the above formula:
3.
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.
While the x coordinate is still found by
Answer: (6, 3)
If we are given 2 points A(a, b) and B(c, d),
the midpoint M, of segment AB has coordinates:
2.
We are given the points A(2, 3) and B(10, 3)
the midpoint of AB, is given by the above formula:
3.
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.
While the x coordinate is still found by
Answer: (6, 3)
<h3>Proof:</h3>
Refer to the attached figure.
There are a couple of ways you can go at this. One is to show the sums of the marked angles are the same, hence ∠B ≅ ∠D. Instead, we're going to show that ΔABD ≅ ΔCDB, hence ∠A ≅ ∠C.
1. AB║DC and BC║AD . . . . given
2. BD is a transversal to both AB║DC and BC║AD . . . . given
3. ∠CBD ≅ ∠ADB . . . . alternate interior angles where a transversal crosses parallel lines are congruent
4. ∠CDB ≅ ∠ABD . . . . alternate interior angles where a transversal crosses parallel lines are congruent
5. BD ≅ BD . . . . reflexive property of congruence
6. ΔABD ≅ ΔCDB . . . . ASA postulate
7. ∠A ≅ ∠C . . . . CPCTC
∠A and ∠C are opposite angles of parallelogram ABCD, so we have shown what you want to have shown.