Ellen is drawing two polygons. One of the polygons has three more angles than the other. What shapes could she be drawing?
2 answers:
The attachment shows different types of polygons.
Now depending on these we have following five possibilities:
Case 1: Triangle and hexagon
If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.
Case 2: Quadrilateral and heptagon
If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.
Case 3: Pentagon and Octagon
If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.
Case 4: Hexagon and Nonagon
If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.
Case 5: Heptagon and Decagon
If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.
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Answer:
- parallel: y = 4x -6
- perpendicular: y = -1/4x +27/4
Step-by-step explanation:
If we want the new line to be written in slope-intercept form, we need to find the new value of the y-intercept. The equation of the line is ...
y = mx +b . . . . . . . for slope m and y-intercept b
Solving for b gives ...
b = y -mx . . . . . . . subtract mx from both sides.
The values of x and y come from the point we want the line to pass through. The value of m will be the same for the parallel line as for the given line: 4. For the perpendicular line, it will be the opposite reciprocal of this: -1/4.
<u>Parallel line</u>
b = 6 -4(3) = 6 -12 = -6
y = 4x -6
Perpendicular line
b = 6 -(-1/4)(3) = 6 +3/4 = 27/4
y = -1/4x +27/4
