Using the triangle similarity theorem, the distance from p to q on road c is calculated as: 2) 975 feet.
What is the triangle similarity theorem?
The Triangle Similarity Theorem states that if the corresponding angles of two triangles are equal, then the triangles are similar, which means that their corresponding side lengths will be proportional.
The triangles shown in the image below are similar to each other based on the AA similarity theorem, thus:
PQ + 650 / 650 = 1200 + 800 / 800
PQ + 650 / 650 = 2000 / 800
PQ + 650 / 650 = 5/2
Cross multiply:
2(PQ + 650) = 5(650)
2PQ + 1300 = 3,250
2PQ = 3,250 - 1,300
2PQ = 1,950
PQ = 975 ft
The answer is: 2) 975 feet.