Question

A quadrilateral-shaped land property is drawn on a coordinate grid. Two adjacent sides of the property lie along the lines y = 4x + 8 and y = – 0.25x – 9, with one corner of the property at the intersection point P of the lines. One of these sides ends at an oak tree located at (–1, 4) and the other side ends at a pine tree located at (4,–10).

What are the coordinates of the point where the two lines intersect?

Answer 1

P(-4,-8)

Explanation:

Given two lines:

`y = 4x + 8;$ and $ \\y = -0.25x - 9`

To determine the point of intersection P of the lines, we equate the two lines and solve for (x,y).

`4x + 8= -0.25x - 9\\4x+0.25x=-9-8\\4.25x=-17\\$Divide both sides by 4.25$\\x=-4\\$Recall:$\\y = 4x + 8\\=4(-4)+8\\=-16+8\\=-8`

Therefore, the intersection point P of the lines is: P(-4,-8)