Question

on a map of the national mall in washington, d.c., the lincoln memorial is located at coordinates (2, 16), and the martin luther king, jr. memorial is located at coordinates (10, 10). a straight line drawn between these two memorials on the map passes through the location of the korean war memorial. the y - coordinate of the korean war memorial is 12. what is the x - coordinate of the korean war memorial on the map? enter your response in the box below.

Explanation:

Step1: Find the slope of the line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(2,16)$ and $(x_2,y_2)=(10,10)$. Then $m=\frac{10 - 16}{10 - 2}=\frac{-6}{8}=-\frac{3}{4}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We use the point $(2,16)$ and $m =-\frac{3}{4}$, so $y-16=-\frac{3}{4}(x - 2)$.

Step3: Substitute the y - coordinate of the Korean War Memorial

Since $y = 12$, we substitute it into the equation $12-16=-\frac{3}{4}(x - 2)$.

Step4: Solve for x

First, simplify the left - hand side: $-4=-\frac{3}{4}(x - 2)$. Multiply both sides by $-\frac{4}{3}$: $-4\times(-\frac{4}{3})=x - 2$. So $\frac{16}{3}=x - 2$. Then $x=\frac{16}{3}+2=\frac{16 + 6}{3}=\frac{22}{3}=6$.

Answer:

6