Make a conjecture. How could the distance formula and slope be used to classify triangles and quadrilaterals in the coordinate plane? Check all that apply.Use the distance formula to measure the lengths of the sides.Use the slope to determine whether opposite sides are parallel.Use the slope to check whether sides are perpendicular and form right angles.Use the distance formula to compare whether opposite sides are congruent.Use the slope to check whether the diagonals are perpendicular to each other.Use the distance formula to compare whether diagonals are congruent.
Answer
A
Use the distance formula to measure the lengths of the sides.
B
Use the slope to determine whether opposite sides are parallel.
C
Use the slope to check whether sides are perpendicular and form right angles.
D
Use the distance formula to compare whether opposite sides are congruent.
E
Use the slope to check whether the diagonals are perpendicular to each other.
F
Use the distance formula to compare whether diagonals are congruent.
Explanation
All six methods can help classify figures in the coordinate plane. The distance formula finds side and diagonal lengths, allowing you to check whether segments are congruent. Slope identifies parallel sides when slopes match and perpendicular sides when their slopes are negative reciprocals, so it can also test for right angles and perpendicular diagonals.
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