Question

5. Consider the line segment in the graph below. Part A: Draw a line segment parallel to AB passing through (-4,-1), that has the same length of AB. Name the line segment MY. Part B: Draw a line segment perpendicular to AB passing through (-3, 4) and intersecting both AB and MY. Name the line segment QU​

Answer 1

See attached

Explanation:

Both of the lines are drawn on the attached

A. .........................

Since lines AB and MY are parallel, and one of the points of parallel line is (-4, -1) the other point is going to have same difference of x and y-coordinates

• A(-3, 2) → M (-4, -1) ⇒ B(2, 4) → Y(1, 1)

Connecting this two points, we get a parallel line to AB

This is a blue line segment on the graph

B. .........................

Perpendicular lines have slopes of negative reciprocal

Considering this and one of the points of a perpendicular line of (-3, 4)

we can calculate the other point.

• Slope of AB = (4-2)/(2 +3) = 2/5
• So slope of the lime QU = -5/2

The other point will have coordinates:

• -3 + 2 = -1 , here 2 is the denominator of the slope

and

• 4 -5 = -1, here -5 is the numerator of the slope

So the line segment is QU with coordinates of (-3, 4) and (-1, -1)

This is red line segment on the graph