The points A, B, and B form a right angle at the point B and the slope of AB is the ratio of BC to AB.
Reasons:
From the diagram, the coordinates of A = (-2, -5)
The length of AB = 5
The length of BC = 10
Solution:
Point B is along the same horizontal line as point A, therefore, given that
AB = 5 units, point B is 5 unite to the right of point A at the coordinate (-2 + 5, -5) = (3, -5)
The coordinates of point [tex]\underline{B = (3, \ -5)}[/tex]
The point C is on the same vertical line as the point B, therefore, given that
BC = 10, the coordinates of point C is the x-coordinates of B and 10 plus the
y-coordinates of the point B, which gives;
C = (3, -5 + 10) = (3, 5)
The coordinates of point [tex]\underline{C = (3, \, 5)}[/tex]
The slope, m, of the line BC is found as follows;
[tex]\displaystyle m =\mathbf{ \frac{Length \ of \ BC}{Length \ of \ AB} }= \frac{10}{5} =2[/tex]
The equation of the line BC is; y - 5 = 2·(x - 3)
Which gives;
y = 2·x - 6 + 5 = 2·x - 1
y = 2·x - 1
The point D is the point where the x-coordinate of a point on the line is 0
Therefore, y-value at D is y = 2 × 0 - 1 = -1
y = -1, and x = 0, at D
The coordinates of [tex]\underline{D = (0,\ -1)}[/tex]
Learn more here:
https://brainly.com/question/18990447
