Question

Show triangle ABC where segment AB is a vertical line, angle C is a right angle, point C is located at (3,2) and the slope of segment AC is 5.

Answer 1

The drawing of the triangle ABC, created with MS Excel is attached

The possible coordinates for points A and B in triangle ΔABC are;

A( -1 , -18 )

B( -1 , 2.8 )

The triangle ABC is constructed using the following steps

The parameters of the triangle ABC are presented as follows;

Segment AB is a vertical line

Angle C is a right angle, therefore, the measure of the angle C, m∠C = 90°

The point C is located at (3, 2)

The slope of the segment AC is 5

The triangle ABC is a right triangle, and the right angle at point C indicates that AC and BC are perpendicular segments

The slope of the segment AC = 5, therefore that the slope of the segment BC can be found using the equation for the relationship between the slope of perpendicular segments, to get;

The slope of BC = -1/5

Taking the point C as being on the right of AB, we get the following coordinate points on AC and BC as follows;

x y-value points on AC y-value points on BC

-1 -18 2.8

0 -13 2.6

1 -8 2.4

2 -3 2.2

3 2 2

The segment AB can be constructed from a selected x-value

The coordinates of the points A and B on the segment AB obtained from the above table of values are; A(-1, -18), B(-1, 2,8)

Please find attached the drawing of the possible triangle ABC, created with MS Excel

The complete question obtained from a similar question found through search can be presented as follows;

Triangle ABC with the following characteristics, is placed on the coordinate plane

• 
  `\overline{AB}` is on a vertical line.

• ∠C is a right angle

• Point C is located at (3, 2)

• The slope of
  `\overline{AC}` is 5

What are the possible coordinates of point A and B?

A(___, ___)

B(___, ___)