Question

Find the distance between the points (-3, -6) and (5,9). Hint: Use the Pythagorean theorem.

Answer 1

Answer:

The distance between the points (-3, -6) and (5, 9) is 15 units.

Step-by-step explanation:

Given the points

• (-3, -6)

• (5, 9)

First, we need to find the distance between the two x-coordinates. For this, we need to count the distance from 0 to another point. Then we just add them together.

i.e.

-3 to get to 0 takes 3 units

0 to 5 takes 5 units

3+5=8 units

Just do the same for y-coordinate

From -6 to 0 takes 6 units

0 to 9 takes 9 units

6+9 = 15 units

Therefore, we get the base and height.

Now using the Pythagoras' Theorem to find the distance:

c² = 8² + 15²

c² = 289

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$c=\sqrt{289},\:c=-\sqrt{289}$

$c=17,\:c=-17$

As the distance can not be negative.

so

• c = 15 units

Thus, the distance between the points (-3, -6) and (5, 9) is 15 units.