Answer:
The coordinates of U is (3, -3)
Explanation:
The given vertices of the parallelogram MULE are;
M(-2, -4), L(0, 7), E(1, 0)
We have;
L(0, 7) and E(1, 0) are the 'y' and x-intercepts of the side LE of the parallelogram MULE
The slope of LE = (0 - 7)/(1 - 0) = -7
With segment MU parallel to LE, we have;
The slope of MU = The slope of LE = -7
The equation of the line segment MU in point and slope form is therefore presented as follows;
y - (-4) = -7 × (x - (-2))
y + 4 = -7·x - 14
y = -7·x - 18
∴ The equation of the line segment MU is 'y = -7·x - 18'
The slope of the line segment ME = (0 - (-4))/(1 - (-2)) = 4/3
For the parallelogram MULE, we have;
The slope of the line segment ME = The slope of the line segment UL
∴ The slope of the line segment UL = 4/3
The equation of the line segment UL in point and slope form is therefore presented as follows;
y - 7 = (4/3)·(x - 0)
∴ y = 4·x/3 + 7
The equation of the line segment UL is 'y = 4·x/3 + 7'
The point 'U' is given by finding the value of 'y' that satisfies the equations of the line segments MU and UL as follows;
The equation for MU is 'y = -7·x - 18'
The equation for UL is 'y = 4·x/3 + 7'
At vertex point 'U', we have;
y = -7·x - 18 = y = 4·x/3 + 7
-7·x - 18 = 4·x/3 + 7
7·x + 4·x/3 = -18 - 7 = -25
(21·x + 4·x)/3 = 25·x/3 = -25
25·x/3 = -25
∴ x = -25 × 3/25 = -3
The x-axis coordinate of the point 'U', x = -3
y = 4·x/3 + 7
∴ y = 4 × (-3)/3 + 7 = -4 + 7 = 3
y = 3
The y-axis coordinate of the point 'U', y = -3
The coordinates of the vertex 'U', (x, y) = (3, -3)