Question

1-3 mathematical literacy and vocabulary
midpoint and distance
problem
what is the distance between a(-2, 3) and b(4, 14)? round to the nearest tenth. justify your steps.
let a(-2, 3) be (x1, y1) and b(4, 14) be (x2, y2).
d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}
write the distance formula.
d = \sqrt{(4 - (-2))^2+(14 - 3)^2}
substitute x1, x2, y1, and y2 into the formula.
d = \sqrt{6^2 + 11^2}
subtract.
d = \sqrt{36 + 121}
square each term.
d = \sqrt{157}
add.
d = 12.53
use a calculator to find the square root.
d = 12.5
round to the nearest tenth.
exercise
what is the distance between a(-5, 5) and b(2, 13)? round to the nearest tenth. justify your steps.
d = \sqrt{(x2 - x1)^2+(y2 - y1)^2}
d = \sqrt{(2 - (-5))^2+(13 - 5)^2}
d = \sqrt{7^2 + 8^2}
d = \sqrt{49 + 64}
d = \sqrt{113}
d = 10.63
d = 10.6

Explanation:

Step1: Write the distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Step2: Substitute the values

Let $A(-5,5)$ be $(x_1,y_1)$ and $B(2,13)$ be $(x_2,y_2)$. Then $d=\sqrt{(2 - (-5))^2+(13 - 5)^2}$

Step3: Subtract inside the square - root

$d=\sqrt{7^2 + 8^2}$

Step4: Square each term

$d=\sqrt{49+64}$

Step5: Add the terms inside the square - root

$d=\sqrt{113}$

Step6: Calculate the square root

$d = 10.63$

Step7: Round to the nearest tenth

$d = 10.6$

Answer:

$10.6$