Question

1. given points a, b, and c located at a(-2,7), b(5,3), and c(-2,-1): (a) plot and label the three points on the given grid. (b) draw in $overline{ab}$ and $overline{ac}$. (c) name the angle that is drawn on the diagram. (d) is the angle from (c) acute or obtuse? how can you tell without using your protractor?

Explanation:

Step1: Plot points

On the coordinate - grid, for point A(-2,7), move 2 units to the left of the y - axis and 7 units up from the x - axis and label it A. For point B(5,3), move 5 units to the right of the y - axis and 3 units up from the x - axis and label it B. For point C(-2, - 1), move 2 units to the left of the y - axis and 1 unit down from the x - axis and label it C.

Step2: Draw line - segments

Use a straight - edge to draw a line - segment connecting points A and B (label it $\overline{AB}$) and a line - segment connecting points A and C (label it $\overline{AC}$).

Step3: Name the angle

The angle formed by $\overline{AB}$ and $\overline{AC}$ with vertex A is named $\angle BAC$.

Step4: Determine angle type

The slope of line AB, $m_{AB}=\frac{y_B - y_A}{x_B - x_A}=\frac{3 - 7}{5+2}=\frac{-4}{7}$. The slope of line AC, since $x_A=x_C=-2$, is a vertical line (undefined slope). By observing the direction of the two lines, the angle $\angle BAC$ is less than 90 degrees. An acute angle is an angle whose measure is less than 90 degrees. So, $\angle BAC$ is acute.

Answer:

(a) Points A(-2,7), B(5,3), C(-2, - 1) are plotted on the grid.
(b) $\overline{AB}$ and $\overline{AC}$ are drawn.
(c) $\angle BAC$
(d) Acute. The angle is less than 90 degrees by observing the direction of the lines $\overline{AB}$ and $\overline{AC}$.