1. Since you want a 1 to 2 ratio, you need a total of three parts, so the fractions you are thinking about are 1/3 and 2/3. Since it says directed line segment XY, we’re thinking from X to Y, so the point K is going to be closer to X.
Create a right triangle.
Find the lengths of the legs.
To go 1/3 of the way along XY, we think about going 1/3 of the x distance and then 1/3 of the Y distance.
The x distance is 6, so we only want to use 1/3 of 6, which is 2. Remember, 2 is not the final answer. We want to go 2 units to the left of Point X, which leaves us at an x-value of 0.
The y distance is 12, and we only want 1/3 of that, which is 4. Once again, 4 is not the value you end at, but the distance you want to go up from Point X. So from-3, we go up 4 to end up at 1.
Altogether, this gives us the coordinate point K(0,1)
3 and 4: Midpoint- find the x and y distances, take half, and then go that distance from the corresponding x and y parts of your original points. Be careful about direction- left is negative, right is positive, up is positive, down is negative. Where you choose to start from matters.
The short cut for finding the midpoint of two values is to add them and divide by 2. So you would need to do this separately for the x values of two points and then for its y values.
5 and 6: Slope is rise over run. (y2-y1)/(x2-x1). Don’t forget to simplify your answer, and negative over a negative is a positive.
7. Perpendicular lines have opposite reciprocal slopes (flip it and add a negative sign, or take it away if the original slope already had one.) For this problem, choose any starting point, then just go up 1 and over 2 from that point (1/2 is the opposite reciprocal slope of -2 from the previous problem). The point you end up at is your other end point.
8. Parallel lines have the same slope. Use 4/5 from problem 6. Pick any point, and just go up 4 and over 5 to get your other endpoint.
9. Create a big rectangle around the whole figure and calculate that whole area first. Then identify all of the extra triangles and rectangles that are being included that you don’t want the area of. Find their areas, and subtract them from the total area that you found at first. What you are left with is the area of the figure.
10. For area, think the same way as 9. For perimeter, you will need to use the pythagorean theorem or distance formula 4 times for each segment. Round to the nearest tenth and add up all of your lengths.
11 and 12. See 5-8.