Answer:
Blank A: (17, 0)
Blank B: (-2, 19)
Explanation:
Blank A:
Step 1: Find the slope of AB:
Before we can find the equation of CD, we'll first need to find the slope of AB
We can do this using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where
- m is the slope,
- (x1, y1) is one point,
- and (x2, y2) is another point.
Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:
m = (14 - (-3)) / (7 - (-10))
m = (14 + 3) / (7 + 10)
m = 17 / 17
m = 1
Thus, the slope of AB is 1.
Step 2: Find the slope of CD:
The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:
m2 = -1 / m1, where
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we know.
Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:
m2 = -1 / 1
m2 = -1
Thus, the slope of CD is -1.
Step 3: Find the y-intercept of CD:
One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where
- (x, y) is any point on the line,
- m is the slope,
- and b is the y-intercept.
Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:
12 = -1(5) + b
12 = -5 + b
17 = b
Thus, the equation of CD is y = -x + 17
For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.
Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:
0 = -x + 17
-17 = -x
17 = x
Thus, the x-coordinate of the x-intercept of CD is 17.
Thus, the coordinates of the x-intercept of CD are (17, 0)
Blank B:
We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:
19 = -(-2) + 17
19 = 2 + 17
19 = 19
Thus, (-2, 19) lies on CD.