Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is 2/5?
2 answers:
Answer:The line p is parallel , n is perpendicular, line m and q are neither parallel not perpendicular.
Explanation:
The slope of given line is .
The slope of parallel line are equal.
Only the slope of line p is which is equal to the slope of given line, therefore the line p is parallel to the given line.
The product of slopes of perpendicular lines is -1.
The slope of n is and the slope of given line is
.
Since the product of slopes is -1, so the line n is perpendicular to the given line.
The slope of m is and the slope of given line is
.
Since the product of slopes is not equal to -1, so the line m is not perpendicular to the given line.
The slope of q is and the slope of given line is
.
Since the product of slopes is not equal to -1, so the line q is not perpendicular to the given line.
Therefore the line m and q are neither parallel not perpendicular.
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2. What we are trying to find here is BH.
3. The second picture shows the "diagonal section", DBFH in another perspective.
4. We notice that HB is the hypothenuse of right triangle DBH.
5. So we can apply the pythegoran theorem to find HB, but first we need to find HD and DB.
6. HD is just a side of the cube so it is 5 units. DB is the diagonal of the base square ABCD, so we find it by applying the pythagorean theorem in right triangle ABD:
6. So we have both HD and DB:
7. Remark: Another way would be to use the generalized Pythagorean theorem, which is as follows:
8. In general, given a right rectangular prism with sides a, b and c, the diagonal is given by
2. What we are trying to find here is BH.
3. The second picture shows the "diagonal section", DBFH in another perspective.
4. We notice that HB is the hypothenuse of right triangle DBH.
5. So we can apply the pythegoran theorem to find HB, but first we need to find HD and DB.
6. HD is just a side of the cube so it is 5 units. DB is the diagonal of the base square ABCD, so we find it by applying the pythagorean theorem in right triangle ABD:
6. So we have both HD and DB:
7. Remark: Another way would be to use the generalized Pythagorean theorem, which is as follows:
8. In general, given a right rectangular prism with sides a, b and c, the diagonal is given by