Back to Exercise: Calculate distance and midpoint on complex plane

Exercises: Calculate Distance and Midpoint on the Complex Plane

Show your work. Express distances as exact values (simplified radicals).

Grade 9·20 problems·~35 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-b-6

Work through problems with immediate feedback

Warm-Up: Review What You Know

In the coordinate plane, what is the distance between the points $(1, 2)$ and $(4, 6)$ ?

$\sqrt{7}$

$5$

$7$

$\sqrt{50}$

What are the coordinates of the midpoint of the segment between $(2, 5)$ and $(6, 1)$ in the coordinate plane?

$(8, 6)$

$(4, 3)$

$(2, 2)$

$(4, 4)$

Compute the modulus $|z - w|$ where $z = 4 + 3i$ and $w = 1 + i$ .

First compute $z - w$ , then find its modulus. Enter the exact value.

Fluency Practice

Find the distance between $z = 5 + 2i$ and $w = 2 + 6i$ .

Distance $= |z - w|$ . Enter the exact simplified value.

Find the distance from $z = -1 + 4i$ to the origin (i.e., to $w = 0$ ).

This equals $|z - 0| = |z|$ . Enter the exact value.

Find the midpoint $M$ of the segment from $z = 3 + 5i$ to $w = 7 + i$ .

$M = \dfrac{z + w}{2} = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $+$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $i$ .

real part of M:

imaginary part of M:

The midpoint of the segment from $z = 2 + 8i$ to $w = -4 + 2i$ is $M = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $+$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $i$ .

real part of M:

imaginary part of M:

Find the distance between $z = 1 + i$ and $w = -2 + 5i$ .

Enter the exact simplified value.

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