Question

Graph the points. Decide whether they are vertices of a right triangle. $$(0,-4),(4,-1),(4,-4)$$

Short answer

The points (0,-4), (4,-1), and (4,-4) when plotted, actually form a right triangle. The triangle is right-angled at the point (4,-4). This was found by verifying Pythagoras theorem as well as checking the slope of the lines.

Step-by-step solution

Plot the Points

Start by plotting the points (0,-4), (4,-1), and (4,-4) on a Cartesian plane. Draw lines to connect these points to form a triangle.

Calculate Slopes

Calculate the slope of the line segment connecting the points (0,-4) and (4,-1), then calculate the slope of the line segment connecting (4,-1) and (4,-4). If these slopes are negative reciprocals of each other, then they form a right angle.

Evaluate

If the two lines are not perpendicular (their slopes are not negative reciprocals), calculate the lengths of all three sides of the triangle using the distance formula and apply Pythagoras theorem to verify if it is a right triangle. If the sum of the squares of the lengths of two of the sides equal the square of the length of the third side, we have a right triangle.