Exercise 43 Page 646

Let's begin with plotting the given points in a coordinate plane. We can connect these two points with a segment.

Since we know that △ JKL is a right triangle with a right angle at the vertex K, we can deduct that the vertex L is lying on the horizontal line y=-2.

If △ JKL is a 45^(∘)-45^(∘)-90^(∘) triangle, then the lengths of segments JK and KL are equal, as this triangle is isosceles. Let's evaluate the length of JK.

Therefore, the third vertex L is 7 units from K either in a positive or a negative direction. However, as we are asked to find the coordinates of L in Quadrant IV we will consider only the first case.

The coordinates of the vertex L are (4,-2).