which point is on the line that passes through point z and is perpendicular to line ab?\n○ (-4, 1)\n○ (1, -2…

which point is on the line that passes through point z and is perpendicular to line ab?\n○ (-4, 1)\n○ (1, -2 )\n○ (2, 0)\n○ (4, 4)

which point is on the line that passes through point z and is perpendicular to line ab?\n○ (-4, 1)\n○ (1, -2 )\n○ (2, 0)\n○ (4, 4)

Answer

Explanation:

Step1: Find slope of line AB

Points $A(-2,4)$ and $B(0,-4)$. Slope formula: $\text{slope} = \frac{y_2-y_1}{x_2-x_1}$ $\text{slope of } AB = \frac{-4-4}{0-(-2)} = \frac{-8}{2} = -4$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal: $\frac{1}{4}$

Step3: Find equation of target line

Line passes through $Z(0,2)$. Use point-slope form $y - y_1 = m(x - x_1)$ $y - 2 = \frac{1}{4}(x - 0)$ → $y = \frac{1}{4}x + 2$

Step4: Test each option

  1. For $(-4,1)$: $y = \frac{1}{4}(-4)+2 = -1+2=1$ ✔️
  2. For $(1,-2)$: $y = \frac{1}{4}(1)+2 = 2.25 \neq -2$ ❌
  3. For $(2,0)$: $y = \frac{1}{4}(2)+2 = 2.5 \neq 0$ ❌
  4. For $(4,4)$: $y = \frac{1}{4}(4)+2 = 3 \neq 4$ ❌

Answer:

$(-4, 1)$