일차함수와 좌표축으로 둘러싸인 도형의 넓이 문제의 정답은?

이 문제의 정답은 1번입니다. 자세한 풀이는 Mathology에서 확인하세요.

어려움일차함수

일차함수와 좌표축으로 둘러싸인 도형의 넓이 문제

두 평행한 일차함수와 좌표축으로 이루어진 도형의 넓이를 이용하여 미지수 k의 값을 찾는 문제입니다.

2026학년도 수능중학교 2학년

문제

두 점 $(-2, -1)$ 과 $(4, 5)$ 를 지나는 직선을 $L_1$ 이라고 하자. 직선 $L_2$ 는 직선 $L_1$ 과 평행하고 점 $(0, k)$ 를 지난다. ( $k \neq 0$ ) 두 직선 $L_1$ , $L_2$ 와 $x$ 축, $y$ 축으로 둘러싸인 도형의 넓이가 15일 때, 가능한 모든 $k$ 값의 합은?

<!-- Ticks and Labels for X-axis -->
<line x1="-5" y1="-0.1" x2="-5" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="-5" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">-5</text>
<line x1="-3" y1="-0.1" x2="-3" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="-3" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">-3</text>
<line x1="-1" y1="-0.1" x2="-1" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="-1" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">-1</text>
<line x1="1" y1="-0.1" x2="1" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="1" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">1</text>
<line x1="3" y1="-0.1" x2="3" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="3" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">3</text>
<line x1="5" y1="-0.1" x2="5" y2="0.1" stroke="#1F2937" stroke-width="0.1"/>
<text x="5" y="-0.3" class="axis-label" text-anchor="middle" transform="scale(0.05, -0.05)">5</text>

<!-- Ticks and Labels for Y-axis -->
<line x1="-0.1" y1="-1" x2="0.1" y2="-1" stroke="#1F2937" stroke-width="0.1"/>
<text x="-0.3" y="-1" class="axis-label" dominant-baseline="middle" transform="scale(0.05, -0.05)">-1</text>
<line x1="-0.1" y1="1" x2="0.1" y2="1" stroke="#1F2937" stroke-width="0.1"/>
<text x="-0.3" y="1" class="axis-label" dominant-baseline="middle" transform="scale(0.05, -0.05)">1</text>
<line x1="-0.1" y1="3" x2="0.1" y2="3" stroke="#1F2937" stroke-width="0.1"/>
<text x="-0.3" y="3" class="axis-label" dominant-baseline="middle" transform="scale(0.05, -0.05)">3</text>
<line x1="-0.1" y1="5" x2="0.1" y2="5" stroke="#1F2937" stroke-width="0.1"/>
<text x="-0.3" y="5" class="axis-label" dominant-baseline="middle" transform="scale(0.05, -0.05)">5</text>

<!-- Origin 'O' -->
<circle cx="0" cy="0" r="0.1" fill="#1F2937"/>
<text x="0.2" y="-0.2" class="axis-label" transform="scale(0.05, -0.05)">O</text>

<!-- Axis Labels (x, y) -->
<text x="5.9" y="-0.3" class="label" text-anchor="end" transform="scale(0.05, -0.05)">x</text>
<text x="-0.3" y="5.9" class="label" text-anchor="end" dominant-baseline="hanging" transform="scale(0.05, -0.05)">y</text>

A(-2,-1)

<circle cx="4" cy="5" r="0.15" fill="#1F2937"/>
<text x="4" y="5.4" class="point-label" text-anchor="middle" transform="scale(0.05, -0.05)">B(4,5)</text>