Three vertices of parallelogram MULE are M (-2, -4), L (0, 7), E (1, 0). Find the coordinates of U.

The coordinates of U is (3, -3)

Step-by-step 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)