Question

which point could be on the line that is parallel to line kl and passes through point m? (-10,0) (-6,2) (0,-6) (8,-10)

Explanation:

Step1: Find the slope of line \(KL\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(K(-6,7)\) and \(L(6,1)\). Then \(m_{KL}=\frac{1 - 7}{6-(-6)}=\frac{-6}{12}=-\frac{1}{2}\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Point \(M(-4,-2)\), and since the line is parallel to \(KL\), \(m =-\frac{1}{2}\). The equation is \(y+2=-\frac{1}{2}(x + 4)\), which simplifies to \(y=-\frac{1}{2}x-4\).

Step3: Check each point

• For \((-10,0)\): \(y=-\frac{1}{2}(-10)-4 = 5 - 4=1

eq0\).

• For \((-6,2)\): \(y=-\frac{1}{2}(-6)-4 = 3 - 4=-1

eq2\).

• For \((0,-6)\): \(y=-\frac{1}{2}(0)-4=-4

eq - 6\).

• For \((8,-10)\): \(y=-\frac{1}{2}(8)-4=-4 - 4=-10\).

Answer:

\((8,-10)\)