A directed segment QR¯¯¯¯¯ with endpoints at Q (2, 1) and R (8, 13) is partitioned from Q to R into a 1:2 ratio at point Z. What are the coordinates of Z? (2, 4)

(4, 5)

(6, 9)

(9, 10)

The coordinate of the point Z is (4, 5)

Step-by-step explanation:

The given information are;

The coordinates of the endpoints of the directed segment QR are Q(2, 1) and R(8, 13)

The ratio of the partition of the directed line segment QR from Q to R = 1:2

The location of the point at the directed line segment is partitioned = Point Z

Therefore, we have;

The proportion of the partition segment QZ to QR is given as follows;

QZ = 1/(1 + 2) × QR  = 1/3·QR

ZR = 2/(1 + 2) × QR  = 2/3·QR

Which gives the coordinate of the point Z as follows;

The coordinate of the point Z = (2 + (8 - 2)×1/3, 1 + (13 - 1)×1/3)

The coordinate of the point Z = (2 + 2, 1 + 4) = (4, 5)

The coordinate of the point Z = (4, 5).

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared