- #1

nycmathguy

- Homework Statement
- Use the distance formula and the Pythagorean theorem in terms of working with perpendicular segments.

- Relevant Equations
- ##distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}##

(leg)^2 + (leg)^2 = (hypotenuse)^2

For easy calculation, I will use a for m_1 and b for m_2 and then back substitute for a and b.

We have (0, 0) and (1, a).

d_1 = sqrt{(1 - 0)^2 + (a - 0)}

d_1 = sqrt{(1)^2 + (a)^2}

d_1 sqrt{1 + a^2}

For d_2, we are going to need (0, 0) and (1, b).

I say d_2 = sqrt{1 + b^2}.

Back-substitute for a and b.

d_1 = sqrt{1 + m_1}

d_2 = sqrt{1 + m_2}

To find the distance from (1, m_1) to (1, m_2), I can use the distance formula or the Pythagorean Theorem.

I don't understand this part of the problem:

"Then use the Pythagorean Theorem to find a relationship m_1 and m_2."

Stuck here.

We have (0, 0) and (1, a).

d_1 = sqrt{(1 - 0)^2 + (a - 0)}

d_1 = sqrt{(1)^2 + (a)^2}

d_1 sqrt{1 + a^2}

For d_2, we are going to need (0, 0) and (1, b).

I say d_2 = sqrt{1 + b^2}.

Back-substitute for a and b.

d_1 = sqrt{1 + m_1}

d_2 = sqrt{1 + m_2}

To find the distance from (1, m_1) to (1, m_2), I can use the distance formula or the Pythagorean Theorem.

I don't understand this part of the problem:

"Then use the Pythagorean Theorem to find a relationship m_1 and m_2."

Stuck here.