Thread: word questions

1.Which geometric figure has two sides with a slope-4/5 and two with 4/5 that has four sides which are all equal in length?

2. If your are given three points that represent the vertices of a triangle PQR, without measuring or drawing a sketch, how would you determine if the triangle is a right triangle. Explain.

Thanks

Originally Posted by euclid2

1.Which geometric figure has two sides with a slope-4/5 and two with 4/5 that has four sides which are all equal in length?

2. If your are given three points that represent the vertices of a triangle PQR, without measuring or drawing a sketch, how would you determine if the triangle is a right triangle. Explain.

Thanks

1) slope -4/5 and slope 4/5 are not negative reciprocls.
If they were, then the figure would have been a square.
As it is, the figure is a parallelogram, or more specifically, a rhombus.

2) Solve for the slopes of the 3 sides.
If there are two slopes that are negative reciprocals, then PQR is a right
triangle.

If two lines are perpendicular, then their slopes are negative reciprocals.

Originally Posted by euclid2

1.Which geometric figure has two sides with a slope-4/5 and two with 4/5 that has four sides which are all equal in length?

2. If your are given three points that represent the vertices of a triangle PQR, without measuring or drawing a sketch, how would you determine if the triangle is a right triangle. Explain.

Thanks

hi!euclid
1) I don't think there is any geometric figure whose all length and slopes are equal.(may be 4
parallel line segments of equal length and slope 4/5 but you can not call the line segment of such figure a side).(may be you wanted to ask something else but you have given a wrong data.May be you wanted to say two sides with slope 4/5 and two with other but equal slope.but in data you gave all slope=4/5).
2)find the distance between the points(using distance formula) and use pythagoras theorem.
Or find the tan of all the angles,you will definitly get infinity for the right angle.
NOTE:tan of angle between line of slope m1 and m2 =mod [(m1-m2)/1+m1m2].