Exercise 1 Page 55

Let's go through the different exercises.

Which sides are perpendicular?

Perpendicular lines have slopes, m_1 and m_2, that are negative reciprocals. This means that the product of their slopes equals - 1: m_1* m_2=- 1 So by finding which slopes makes the formula true, we determine which sides are perpendicular.

Finding the vertices

The vertices of the triangle will be where the lines making up the triangle's sides intersect. By setting two of the equations equal to each other, we can find the x-coordinate where they intersect. Substituting this value into one of those equations, we can find the corresponding y-value. To find all three vertices we will have to do this procedure three times.

Finding the perimeter

The perimeter of the triangle will be the sum of its three sides. When we know the coordinates of the vertices, we can use the Distance Formula to find the length of each of the sides.

Finding the Area

The area of a triangle is the base times it's height divided by 2. The height is always perpendicular to the base and, since we are dealing with a right triangle, we know that the legs, or catheti, make up the height and base.