To plot the points on a graph, we need to:
1. Start by plotting point A (-8, 4) on the graph.
2. Plot point B (-4, -3) on the graph.
3. Plot point C (3, -3) on the graph.
4. Plot point D (5, 6) on the graph.
Joining these points forms a quadrilateral (a four-sided shape).
To draw AC, simply connect point A to point C.
To draw BD, connect point B to point D.
The intersection of BD with the x-axis will be a point on the x-axis (y-coordinate = 0).
Let's call this point E. To find the coordinates of point E, we need to find the x-intercept of the line BD.
Using the slope-intercept form (y = mx + b), we can find the equation of line BD:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line (either B or D).
Let's use point B (-4, -3):
y + 3 = m(x + 4)
We can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = B (-4, -3) and (x2, y2) = D (5, 6):
m = (6 - (-3)) / (5 - (-4))
= 9 / 9
= 1
Now we can write the equation of line BD:
y + 3 = x + 4
To find the x-intercept (point E), set y = 0:
0 + 3 = x + 4
-4 = x
So, point E has coordinates (-4, 0).
The figure obtained by joining the points is a quadrilateral (a four-sided shape).
