Question

Is the line through point P (8,10) and (10,11) perpendicular to the line through point (-8,1) and (-7,3)?

A. YES, their slopes are equal.
B. YES, their slopes have a product of -1.
C. NO, their slopes are not opposite reciprocal.
D. NO, their slopes are not equal.

Answer 1

The slopes of the two lines in question are 0.5 and 2, respectively. Since their product is not -1, the lines are not perpendicular. The correct answer is C. NO, their slopes are not opposite reciprocals.

Step-by-step explanation:

Let's determine if the line through points P (8,10) and (10,11) is perpendicular to the line through points (-8,1) and (-7,3). The slope of a line passing through two points (x1, y1) and (x2, y2) is calculated using the formula (y2 - y1) / (x2 - x1).

For the first line through points P (8,10) and (10,11), the slope is (11 - 10) / (10 - 8) = 1 / 2 = 0.5.

The second line through points (-8,1) and (-7,3), the slope is (3 - 1) / (-7 - (-8)) = 2 / 1 = 2.

To be perpendicular, the slopes of two lines need to have a product of -1, when multiplied together (they are opposite reciprocals of each other). In this case, the product of the slopes is 0.5 * 2 = 1, which is not equal to -1. Therefore, the lines are not perpendicular.

The correct answer is C. NO, their slopes are not opposite reciprocals.