Question

use the 5 - by - 5 square lattice shown, with the line segment (overline{ab}). list all the points (c) of the lattice that make (angle bac) the following kinds of angle. do not include points (a) or (b) in any of your answers.
(a) a right angle
(type a whole number. use a comma to separate answers as needed.)

Explanation:

Step1: Recall right angle condition

For $\angle BAC$ to be right, $\overrightarrow{AB} \perp \overrightarrow{AC}$, so their dot product is 0. First, assign coordinates: Let $A = (1,2)$ (point 16) and $B = (3,2)$ (point 18).

Step2: Define point C coordinates

Let $C=(x,y)$ be a lattice point (not A/B). $\overrightarrow{AB}=(2,0)$, $\overrightarrow{AC}=(x-1,y-2)$.

Step3: Apply perpendicularity condition

Dot product: $2(x-1) + 0(y-2)=0 \implies x-1=0 \implies x=1$.

Step4: List valid C points

Points with $x=1$ (column 1) excluding A (16): 1, 6, 11, 21.

Answer:

1, 6, 11, 21