Given a line segment with end points a (0,0) and b (6,8), find point c (x, y) that the triangle vertices a, b and c has an area of 25 square units?

C(6.25 , 0)

Step-by-step explanation:

Draw the diagram

A is at (0,0)

B is at (6,8)

Draw a line from A to B.

Put a large dot where (0,6) is. Call this D

Draw BD

Draw another line from (0,0) to just beyond (6,0) Call this C. Draw in BC

What You Have Drawn

The height of the triangle is BD and it is 8. That comes from B which is (6,8)

Solve

Formula

Area = 1/2 * B * H

Area = 25

H = 8

Area = 1/2 B * H

25 = 1/2 * B * 8             Switch sides

1/2  * B * 8 = 25            Combine factors on the left.

4 B = 25                       Divide both sides by 4

4B/4  = 25/4        

B = 6.25

What that means is that AC is 6.25 units long and is on the x axis

C is C(6.25,0)

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

-81 -56 -27 0 81

step-by-step explanation: